J. Banasiak We discuss a mixed-suspension, mixed-product removal crystallizer operated at thermodynamic equilibrium. We derive and discuss the mathematical model based on population and mass balance equations and prove local existence and uniqueness of solutions using the method of characteristics. We also discuss the global existence of solutions for continuous and batch mode. Finally, a numerical simulation of a continuous crystallizer in steady state is presented. Copyright © 2015 John Wiley & Sons, Ltd.

]]>We study the existence and multiplicity of solutions for a nonlinear boundary value problem subject to perturbations of impulsive terms. Under suitable assumptions on the potential of the nonlinearity, the existence of one or two solutions is established. Our approach is based on a local minimum theorem and a two non-zero critical points for differentiable functionals. Copyright © 2015 John Wiley & Sons, Ltd.

]]>In this paper, the spectral analysis of a singular dissipative fourth order differential operator in lim-4 case with finite transmission conditions is investigated. For this purpose, the inverse operator with explicit form is used. Finally, with the help of Livšic's theorem, it is proved that all root vectors of the fourth order dissipative operator in lim-4 case with finite transmission conditions are complete in the Hilbert space. Copyright © 2015 John Wiley & Sons, Ltd.

]]>We investigate in this paper the solutions and the periodicity of the following rational systems of difference equations of three-dimensional

with initial conditions *x*_{−2},*x*_{−1},*x*_{0},*y*_{−2},*y*_{−1},*y*_{0},*z*_{−2},*z*_{−1}and*z*_{0} are nonzero real numbers. Copyright © 2015 John Wiley & Sons, Ltd.

In this paper, for a coupled system of one-dimensional wave equations with Dirichlet boundary controls, we show that the controllability of classical solutions implies the controllability of weak solutions. This conclusion can be applied in proving some results that are hardly obtained by a direct way in the framework of classical solutions. For instance, we strictly derive the necessary conditions for the exact boundary synchronization by two groups in the framework of classical solutions for the coupled system of wave equations. Copyright © 2015 John Wiley & Sons, Ltd.

]]>In this paper, we are concerned with the existence of infinitely many solutions for the following fractional Hamiltonian systems

where , , and . The novelty of this paper is that, relaxing the conditions on the potential function *W*(*t*,*x*), we obtain infinitely many solutions via critical point theory. Our results generalize and improve some existing results in the literature. Copyright © 2015 John Wiley & Sons, Ltd.

We study the exact solutions of the Emden–Fowler equations and generalize the *n* = 1 and *n* = 5 Lane–Emden equations. We analyze the series approximations and show that explicit formulas can be written for new classes of equations. Copyright © 2015 John Wiley & Sons, Ltd.

M. Otani Dedicated to Messoud Efendiev on the occasion of his 60th birthday

For the deceptively innocent case of monomolecular reactions, only, we embark on a systematic mathematical analysis of the steady-state response to perturbations of reaction rates. Our *structural sensitivity analysis* is based on the directed graph structure of the monomolecular reaction network, only. In fact our function-free approach does not require numerical input. We work with general, not necessarily monotone reaction rate functions. Based on the graph structure alone, we derive which steady-state concentrations and reaction fluxes are sensitive to, and thus affected by, a rate change—and which are not. Moreover we establish a transitivity property for the influence of a rate perturbation, at any reaction, on all reaction fluxes. The results and concepts developed here, from a mathematical view point, are of applied relevance including metabolic networks in biology; see our companion paper quoted below. Copyright © 2015 John Wiley & Sons, Ltd.

In this paper, we will study the lower bounds of the life span (the maximal existence time) of solutions to the initial-boundary value problems with small initial data and zero Neumann boundary data on exterior domain for one-dimensional general quasilinear wave equations *u*_{tt}−*u*_{xx}=*b*(*u*,*D**u*)*u*_{xx}+*F*(*u*,*D**u*). Our lower bounds of the life span of solutions in the general case and special case are shorter than that of the initial-Dirichlet boundary value problem for one-dimensional general quasilinear wave equations. We clarify that although the lower bounds in this paper are same as that in the case of Robin boundary conditions obtained in the earlier paper, however, the results in this paper are not the trivial generalization of that in the case of Robin boundary conditions because the fundamental Lemmas 2.4, 2.5, 2.6, and 2.7, that is, the priori estimates of solutions to initial-boundary value problems with Neumann boundary conditions, are established differently, and then the specific estimates in this paper are different from that in the case of Robin boundary conditions. Another motivation for the author to write this paper is to show that the well-posedness of problem is the essential precondition of studying the lower bounds of life span of classical solutions to initial-boundary value problems for general quasilinear wave equations. The lower bound estimates of life span of classical solutions to initial-boundary value problems is consistent with the actual physical meaning. Finally, we obtain the sharpness on the lower bound of the life span in the general case and in the special case. Copyright © 2015 John Wiley & Sons, Ltd.

The paper explores an eco-epidemiological model of a predator–prey type, where the prey population is subject to infection. The model is basically a combination of S-I type model and a Rosenzweig–MacArthur predator–prey model. The novelty of this contribution is to consider different competition coefficients within the prey population, which leads to the emergent carrying capacity. We explicitly separate the competition between non-infected and infected individuals. This emergent carrying capacity is markedly different to the explicit carrying capacities that have been considered in many eco-epidemiological models. We observed that different intra-class and inter-class competition can facilitate the coexistence of susceptible prey-infected prey–predator, which is impossible for the case of the explicit carrying capacity model. We also show that these findings are closely associated with bi-stability. The present system undergoes bi-stability in two different scenarios: (a) bi-stability between the planner equilibria where susceptible prey co-exists with predator or infected prey and (b) bi-stability between co-existence equilibrium and the planner equilibrium where susceptible prey coexists with infected prey; have been discussed. The conditions for which the system is to be permanent and the global stability of the system around disease-free equilibrium are worked out. Copyright © 2015 John Wiley & Sons, Ltd.

]]>It is preliminarily known that *Aedes* mosquitoes be very close to humans and their dwellings also give rises to a broad spectrum of diseases: dengue, yellow fever, and chikungunya. In this paper, we explore a multi-age-class model for mosquito population secondarily classified into indoor–outdoor dynamics. We accentuate a novel design for the model in which periodicity of the affecting time-varying environmental condition is taken into account. Application of optimal control with collocated measure as apposed to widely used prototypic smooth time-continuous measure is also considered. Using two approaches, least square and maximum likelihood, we estimate several involving undetermined parameters. We analyze the model enforceability to biological point of view such as existence, uniqueness, positivity, and boundedness of solution trajectory, also existence and stability of (non)trivial periodic solution(s) by means of the basic mosquito offspring number. Some numerical tests are brought along at the rest of the paper as a compact realistic visualization of the model. Copyright © 2015 John Wiley & Sons, Ltd.

Bacterial biofilms are microbial depositions on immersed surfaces. Their mathematical description leads to degenerate diffusion-reaction equations with two non-Fickian effects: (i) a porous medium equation like degeneracy where the biomass density vanishes and (ii) a super-diffusion singularity if the biomass density reaches its threshold density. In the case of multispecies interactions, several such equations are coupled, both in the reaction terms and in the nonlinear diffusion operator. In this paper, we generalize previous work on existence and uniqueness of solutions of this type of models and give a general, relatively easy to apply criterion for well-posedness. The use of the criterion is illustrated in several examples from the biofilm modeling literature. Copyright © 2015 John Wiley & Sons, Ltd.

]]>We investigate the stability of two-dimensional periodic solutions to magnetohydrodynamics equations in the class of three-dimensional periodic solutions. We show the existence of global, strong three-dimensional solutions to magnetohydrodynamics equations, which are close to two-dimensional solutions. The advantage of our approach is that neither these solutions nor the external forces have to vanish at infinity. Copyright © 2015 John Wiley & Sons, Ltd.

]]>In the present paper, we study the problem of multiple non semi-trivial solutions for the following systems of Kirchhoff-type equations with discontinuous nonlinearities

- (1.1)

where *F*∈*C*^{1}(*R*^{N}×*R*^{+}×*R*^{+},*R*),*V*∈*C*(*R*^{N},*R*),

and

By establishing a new index theory, we obtain some multiple critical point theorems on product spaces, and as applications, three multiplicity results of non semi-trivial solutions for (1.1) are obtained. Copyright © 2015 John Wiley & Sons, Ltd.

]]>We study the small-data Cauchy problem for *n*-dimensional Stokes damped Rosenau equation. Under some assumptions, we prove the global existence and uniqueness of the small-amplitude solution by utilizing the contraction mapping principle and study the asymptotic behavior of the solution. Copyright © 2015 John Wiley & Sons, Ltd.

Let *n*≥3, Ω be a strongly Lipschitz domain of and *L*_{Ω}:=−Δ+*V* a Schrödinger operator on *L*^{2}(Ω) with the Dirichlet boundary condition, where Δ is the Laplace operator and the nonnegative potential *V* belongs to the reverse Hölder class for some *q*_{0}>*n*/2. Assume that the growth function satisfies that *ϕ*(*x*,·) is an Orlicz function, (the class of uniformly Muckenhoupt weights) and its uniformly critical lower type index , where and *μ*_{0}∈(0,1] denotes the critical regularity index of the heat kernels of the Laplace operator Δ on Ω. In this article, the authors first show that the heat kernels of *L*_{Ω} satisfy the Gaussian upper bound estimates and the Hölder continuity. The authors then introduce the ‘geometrical’ Musielak–Orlicz–Hardy space via , the Hardy space associated with on , and establish its several equivalent characterizations, respectively, in terms of the non-tangential or the vertical maximal functions or the Lusin area functions associated with *L*_{Ω}. All the results essentially improve the known results even on Hardy spaces with *p*∈(*n*/(*n* + *δ*),1] (in this case, *ϕ*(*x*,*t*):=*t*^{p} for all *x*∈Ω and *t*∈[0,*∞*)). Copyright © 2015 John Wiley & Sons, Ltd.

In this paper, we prove the existence and uniqueness of the local mild solution to the Cauchy problem of the *n*-dimensional (*n*≥3) Wigner–Poisson–BGK equation in the space of some integrable functions whose inverse Fourier transform are integrable. The main difficulties in establishing mild solution are to derive the boundedness and locally Lipschitz properties of the appropriate nonlinear terms in the Wiener algebra. Copyright © 2015 John Wiley & Sons, Ltd.

In this paper, a parameter identification method to determine surface shortwave fluxes using temperature and thickness measurements of sea ice in CHINARE 2006 is presented. Adopting a new standard for the calculation of the thermodynamic properties of seawater named TEOS-10, the surface shortwave fluxes are calculated by the temperature and thickness observations that were measured at Nella Fjord around Zhongshan Station, Antarctica. New simulations for temperature profiles in a different measurement period are performed by three parameterization schemes including the present method, Zillman and Shine. All numerical results are compared with *in situ* measurements. Results show that better simulations of the surface shortwave radiations and temperature distributions are possible with the identification method than Zillman and Shine. Therefore this method is valid, and the obtained shortwave radiation function can be applied in sea ice modeling. Copyright © 2015 John Wiley & Sons, Ltd.

We consider the initial and initial-boundary value problems for a one-dimensional *p*th power Newtonian fluid in unbounded domains with general large initial data. We show that the specific volume and the temperature are bounded from below and above uniformly in time and space and that the global solution is asymptotically stable as the time tends to infinity. Copyright © 2015 John Wiley & Sons, Ltd.

In this paper, we propose a discrete viral infection model with a general incidence rate. The discrete model is derived from a continuous case by using a 'mixed' Euler method, which is a mixture of both forward and backward Euler methods. We prove that the mixed Euler method preserves the qualitative properties of the corresponding continuous system, such as positivity, boundedness, and global behaviors of solutions. Furthermore, the model and mathematical results presented in another previous study are extended and generalized. Copyright © 2015 John Wiley & Sons, Ltd.

]]>In this study, the nonlinear fractional partial differential equations have been defined by the modified Riemann–Liouville fractional derivative. By using this fractional derivative and traveling wave transformation, the nonlinear fractional partial differential equations have been converted into nonlinear ordinary differential equations. The modified trial equation method is implemented to obtain exact solutions of the nonlinear fractional Klein–Gordon equation and fractional clannish random walker's parabolic equation. As a result, some exact solutions including single kink solution and periodic and rational function solutions of these equations have been successfully obtained. Copyright © 2015 John Wiley & Sons, Ltd.

]]>In this paper, new and efficient numerical method, called as Chebyshev wavelet collocation method, is proposed for the solutions of generalized Burgers–Huxley equation. This method is based on the approximation by the truncated Chebyshev wavelet series. By using the Chebyshev collocation points, algebraic equation system has been obtained and solved. Approximate solutions of the generalized Burgers–Huxley equation are compared with exact solutions. These calculations demonstrate that the accuracy of the Chebyshev wavelet collocation solutions is quite high even in the case of a small number of grid points. Copyright © 2015 John Wiley & Sons, Ltd.

]]>In this paper, we prove the unique continuation property for the weak solution of the plate equation with the low regular coefficient. Then, we apply this result to study the global attractor for the semilinear plate equation with a localized damping. Copyright © 2015 John Wiley & Sons, Ltd.

]]>A coefficient inverse problem for a parabolic equation is considered. Using a Carleman weight function, a globally strictly convex cost functional is constructed for this problem. Copyright © 2015 John Wiley & Sons, Ltd.

]]>This paper is concerned with the oscillation of numerical solution for the Nicholson's blowflies model. Using two kinds of *θ*-methods, namely, the linear *θ*-method and the one-leg *θ*-method, several conditions under which the numerical solution oscillates are derived. Moreover, it is shown that every non-oscillatory numerical solution tends to equilibrium point of the original continuous-time model. Finally, numerical experiments are provided to illustrate the analytical results. Copyright © 2015 John Wiley & Sons, Ltd.

C. Miao In this paper, we are concerned with the 1D Cauchy problem of the compressible Navier–Stokes equations with the viscosity *μ*(*ρ*) = 1+*ρ*^{β}(*β*≥0). The initial density can be arbitrarily large and keep a non-vacuum state at far fields. We will establish the global existence of the classical solution for 0≤*β* < *γ* via a priori estimates when the initial density contains vacuum in interior interval or is away from the vacuum. We will show that the solution will not develop vacuum in any finite time if the initial density is away from the vacuum. To study the well-posedness of the problem, it is crucial to obtain the upper bound of the density. Some new weighted estimates are applied to obtain our main results. Copyright © 2015 John Wiley & Sons, Ltd.

We study second-order equations and systems on non-Lipschitz domains including mixed boundary conditions. The key result is interpolation for suitable function spaces. From this, elliptic and parabolic regularity results are deduced by means of Šneı̆berg's isomorphism theorem. Copyright © 2015 John Wiley & Sons, Ltd.

]]>This work is a natural continuation of two other works in which a mathematical model has been studied. This model is based on age-cycle length structured cell population. The cellular mitosis is mathematically described by a non-compact boundary condition. We investigate the asymptotic behavior of the generated semigroup, and we prove that the cell population possesses *Asynchronous Growth Property*. Copyright © 2015 John Wiley & Sons, Ltd.

In this paper, we deal with invex equilibrium problems (IEPs for short). When the constraint set is compact convex, an existence result of solutions is obtained by Schauder's fixed point theorem. If the constraint set is closed invex, we introduce the concept of relaxed *α*–*η* pseudomonotone mappings and prove some existence results of solutions for the (IEPs), which extend and generalize several well-known results in many respects. Moreover, we present that if the IEPs are applied to hemivariational inequalities problems, the conditions can be weakened. Copyright © 2015 John Wiley & Sons, Ltd.

In this article, we prove the local existence of a unique solution to a nonlocal in time and space evolution equation with a time nonlocal nonlinearity of exponential growth. Moreover, under some suitable conditions on the initial data, it is shown that local solutions experience blow-up. The time profile of the blowing-up solutions is also presented. Copyright © 2015 John Wiley & Sons, Ltd.

]]>In this paper, we consider a nonlinear age structured McKendrick–von Foerster population model with diffusion term. Here we prove existence and uniqueness of the solution of the equation. We consider a particular type of nonlinearity in the renewal term and prove Generalized Relative Entropy type inequality. Longtime behavior of the solution has been addressed for both linear and nonlinear versions of the equation. In linear case, we prove that the solution converges to the first eigenfunction with an exponential rate. In nonlinear case, we have considered a particular type of nonlinearity that is present in the mortality term in which we can predict the longtime behavior. Copyright © 2015 John Wiley & Sons, Ltd.

]]>With the aid of Lenard recursion equations, we derive the Wadati–Konno–Ichikawa hierarchy. Based on the Lax matrix, an algebraic curve of arithmetic genus *n* is introduced, from which Dubrovin-type equations and meromorphic function *φ* are established. The explicit theta function representations of solutions for the entire WKI hierarchy are given according to asymptotic properties of *φ* and the algebro-geometric characters of . Copyright © 2015 John Wiley & Sons, Ltd.

This paper is concerned with the existence of solutions to a class of *p*(*x*)-Kirchhoff-type equations with Dirichlet boundary data as follows:

By means of variational methods and the theory of the variable exponent Sobolev spaces, we establish some conditions on the existence of solutions. Copyright © 2015 John Wiley & Sons, Ltd.

This paper deals with the long-term properties of the thermoelastic nonlinear string-beam system related to the well-known Lazer–McKenna suspension bridge model

- (0.1)

In particular, no mechanical dissipation occurs in the equations, because the loss of energy is entirely due to thermal effects. The existence of regular global attractors for the associated solution semigroup is proved (without resorting to a bootstrap argument) for time-independent supplies *f*,*g*,*h* and any . Copyright © 2015 John Wiley & Sons, Ltd.

In thiswork,we present two new(3+1)-dimensional nonlinear equationswith Korteweg-de Vries equation constituting its main part. We show that the dispersive relation is distinct for each model, whereas the phase shift remains the same. We determine multiple solitons solutions, with distinct physical structures, for each established equation. The architectures of the simplified Hirota's method is implemented in this paper. The constraint conditions that fall out which must remain valid in order for themultiple solitons to exist are derived.Copyright © 2015 John Wiley & Sons, Ltd.

]]>This paper is concerned with a suspension bridge equation with memory effects , defined in a bounded domain of . For the suspension bridge equation without memory, there are many classical results. Existing results mainly devoted to existence and uniqueness of a weak solution, energy decay of solution and existence of global attractors. However the existence of global attractors for the suspension bridge equation with memory was no yet considered. The object of the present paper is to provide some results on the well-posedness and long-time behavior to the suspension bridge equation in a more with past history. Copyright © 2015 John Wiley & Sons, Ltd.

]]>In this paper, we first establish some user-friendly versions of fixed-point theorems for the sum of two operators in the setting that the involved operators are not necessarily compact and continuous. These fixed-point results generalize, encompass, and complement a number of previously known generalizations of the Krasnoselskii fixed-point theorem. Next, with these obtained fixed-point results, we study the existence of solutions for a class of transport equations, the existence of global solutions for a class of Darboux problems on the first quadrant, the existence and/or uniqueness of periodic solutions for a class of difference equations, and the existence and/or uniqueness of solutions for some kind of perturbed Volterra-type integral equations. Copyright © 2015 John Wiley & Sons, Ltd.

]]>The purpose of this paper is to give a proof of global existence of solutions for Gierer–Meinhardt systems with homogeneous Neumann boundary conditions. Our technique is based on Lyapunov functional argument that yields the uniform boundedness of solutions. The asymptotic behaviour of the solutions under suitable conditions is also studied. Moreover, under reasonable conditions on the exponents of the nonlinear term, we show the blow up in finite time of the solutions for the considered system. These results are valid for any positive initial data in , without any differentiability conditions. Copyright © 2015 John Wiley & Sons, Ltd.

]]>This paper studies the Neimark–Sacker bifurcation of a diffusive food-limited model with a finite delay and Dirichlet boundary condition by the backward Euler difference scheme, Crank-Nicolson difference scheme, and nonstandard finite-difference scheme. The existence of Neimark-Sacker bifurcation at the equilibrium is obtained. Our results show that Crank-Nicolson and nonstandard finite-difference schemes are superior to the backward Euler difference scheme under the means of describing approximately the dynamics of the original system. Finally, numerical examples are provided to illustrate the analytical results. Copyright © 2015 John Wiley & Sons, Ltd.

]]>This paper is devoted to global asymptotic stability of cellular neural networks with impulses and multi-proportional delays. First, by means of the transformation *v*_{i}(*t*) = *u*_{i}(*e*^{t}), the impulsive cellular neural networks with proportional delays are transformed into impulsive cellular neural networks with the variable coefficients and constant delays. Second, we prove the global exponential stability of the latter by nonlinear measure, and that the exponential stability of the latter implies the asymptotic stability of the former. We furthermore provide a sufficient condition to the existence, uniqueness, and the global asymptotic stability of the equilibrium point of the former. Our results are generalizations of some existing ones. Finally, an example and its simulation are presented to illustrate effectiveness of our method. Copyright © 2015 John Wiley & Sons, Ltd.

The maximum-likelihood expectation-maximization (EM) algorithm has attracted considerable interest in single-photon emission computed tomography, because it produces superior images in addition to be being flexible, simple, and allowing a physical interpretation. However, it often needs a large number of calculations because of the algorithm's slow rate of convergence. Therefore, there is a large body of literature concerning the EM algorithm's acceleration. One of the accelerated means is increasing an overrelaxation parameter, whereas we have not found any analysis in this method that would provide an immediate answer to the questions of the convergence. In this paper, our main focus is on the continuous version of an accelerated EM algorithm based on Lewitt and Muehllenner. We extend their conclusions to the infinite-dimensional space and interpret and analyze the convergence of the accelerated EM algorithm. We also obtain some new properties of the modified algorithm. Copyright © 2015 John Wiley & Sons, Ltd.

]]>We establish traveling wave solutions for the combustion model of a shear flow in a cylinder. We study two cases: the infinite Lewis number and an arbitrary Lewis number. For the infinite Lewis number, we establish the existence of traveling wave fronts for both non-minimal and minimal speeds. For an arbitrary Lewis number, we establish the uniform bounds and exponential decay rates. Copyright © 2015 John Wiley & Sons, Ltd.

]]>In this paper, we study a class of integral boundary value problem for fractional order impulsive differential equations, where both the nonlinearity and the impulsive terms contain the fractional order derivatives. By using fixed-point theorems, the existence results of solution for the boundary value problem are established. Finally, some examples are presented to illustrate the existence results. Copyright © 2015 John Wiley & Sons, Ltd.

]]>This paper presents a study of immiscible compressible two-phase, such as water and gas, flow through double porosity media. The microscopic model consists of the usual equations derived from the mass conservation laws of both fluids, along with the standard Darcy–Muskat law relating the velocities to the pressure gradients and gravitational effects. The problem is written in terms of the phase formulation, that is, where the phase pressures and the phase saturations are primary unknowns. The fractured medium consists of periodically repeating homogeneous blocks and fractures, where the absolute permeability of the medium becomes discontinuous. Consequently, the model involves highly oscillatory characteristics. The major difficulties related to this model are in the nonlinear degenerate structure of the equations, as well as in the coupling in the system. We obtain the convergence of the solutions, and a macroscopic model of the problem is constructed using the notion of two-scale convergence combined with the dilatation technique. Copyright © 2015 John Wiley & Sons, Ltd.

]]>E. Sanchez-Palencia In this paper, we investigate the dynamic of DNA described via DNA double-stranded model with transverse and longitudinal motions. This model admits solitary, soliton, periodic, or chirped wave solution. It is justified that the most admissible physical solution is the soliton or chirped wave solution. The stability analysis of all these solutions is performed by using the Sturm–Liouville problem and the topological invariance. We found that soliton and chirped waves are unstable so that the unbounded amplitude may occur. In the view of these models, damage of DNA membrane or bases may occur under small disturbance. Also, the suggested models will be indispensable when inhomogeneity or medium dissipation is taken into account. Copyright © 2015 John Wiley & Sons, Ltd.

]]>G. R. Franssens In this paper, we present an explicit construction for the fundamental solution of the heat operator, the Schrödinger operator, and related first-order parabolic Dirac operators on a class of some conformally flat non-orientable orbifolds. More concretely, we treat a class of projective cylinders and tori where we can study parabolic monogenic sections with values in different pin bundles. We present integral representation formulas together with some elementary tools of harmonic analysis that enable us to solve boundary value problems on these orbifolds. Copyright © 2015 John Wiley & Sons, Ltd.

]]>Mathematical models are of great value in epidemiology to help understand the dynamics of the various infectious diseases, as well as in the conception of effective control strategies. The classical approach is to use differential equations to describe, in a quantitative manner, the spread of diseases within a particular population. An alternative approach is to represent each individual in the population as a string or vector of characteristic data and simulate the contagion and recovery processes by computational means. This type of model, referred in the literature as MBI (models based on individuals), has the advantage of being flexible as the characteristics of each individual can be quite complex, involving, for instance, age, sex, pre-existing health conditions, environmental factors, social habits, etc. However, when it comes to simulations involving large populations, MBI may require a large computational effort in terms of memory storage and processing time. In order to cope with the problem of heavy computational effort, this paper proposes a parallel implementation of MBI using a graphics processor unit compatible with CUDA. It was found that, even in the case of a simple susceptible–infected–recovered model, the computational gains in terms of processing time are significant. Copyright © 2015 John Wiley & Sons, Ltd.

]]>The new type of nonlinear integral inequalities of Volterra–Fredholm type for discontinuous functions is investigated. Then, by using these inequalities and Schaefer fixed-point theorem, we present new existence results for impulsive semilinear differential equations with nonlocal conditions. Moreover, the compactness of solution sets can be shown in some certain conditions. Copyright © 2015 John Wiley & Sons, Ltd.

]]>In this paper, by using critical point theory in combination with periodic approximations, we obtain some new sufficient conditions on the nonexistence and existence of homoclinic solutions for a class of periodic difference equations. Unlike the existing literatures that always assume that the nonlinear terms are only either superlinear or asymptotically linear at , but superlinear at 0, our nonlinear term can mix superlinear nonlinearities with asymptotically linear ones at both and 0. To the best of our knowledge, this is the first time to consider the homoclinic solutions of this class of difference equations with mixed nonlinearities. Our results are necessary in some sense, and extend and improve some existing ones even for some special cases. Copyright © 2015 John Wiley & Sons, Ltd.

]]>This paper is concerned with a non-selective harvesting predator–prey model with Hassell–Varley type functional response and impulsive effects. By using the fixed point theory based on monotone operator, some simple conditions are obtained for the existence of at least one positive periodic solution of the model. The existence result of this paper implies that the functional response on prey does not influence the existence of positive periodic solution of the model, which completes some results given in recent years. Further, by applying the comparison theorem in impulsive differential equations and constructing a suitable Lyapunov functional, the permanence and global attractivity of the model are also investigated. The main results in this paper extend, complement, and improve the previously known result. And some examples and numerical simulations are given to illustrate the feasibility and effectiveness of the main results. Copyright © 2015 John Wiley & Sons, Ltd.

]]>In a previous work on perturbation theory in population dynamics, we showed several plausible situations of preservation of the biodiversity. We give now an improved version of the method exhibiting a phenomenon of emergence of structured diversity. We display several (plausible in ethological or sociological contexts) examples of small modifications of the demographic equations that are emergent, that is, they lead to a limit state (the attractor) where the ‘spectators’ (i.e. to the individuals not concerned with the modification) vanish. In other words, even if the modification involves only a small number of individuals initially, the final pattern involves all the individuals. This behavior is easily understood in cases when the modification is concerned with some kind of symbiotic behavior, as it induces an advantage with respect to the ‘spectators’. But the phenomenon is very much general; we give examples of emergence in other contexts, involving predator/pray relations or other entangled relations, including an experimentally known example of subspecies of *Escherichia coli*. Copyright © 2015 John Wiley & Sons, Ltd.

Nonlinear diffusion equation with a polynomial source is considered. The Painlevé analysis of equation has been studied. Exact traveling wave solutions in the simplest cases have been found. Copyright © 2015 John Wiley & Sons, Ltd.

]]>In this paper, we study an American option-pricing model with an uncertain volatility. Some properties for the option price are derived. Particularly, a global spread for the option price is proved when the volatility depends on the underlying security and time. This result confirms the observed fact from the real financial data in option markets. Copyright © 2015 John Wiley & Sons, Ltd.

]]>This paper is concerned with the multidimensional Cahn–Hilliard equation with a constraint. The existence of periodic solutions of the problem is mainly proved under consideration by the viscosity approach. More precisely, with the help of the subdifferential operator theory and Schauder fixed point theorem, the existence of solutions to the approximation of the original problem is shown, and then the solution is obtained by using a passage-to-limit procedure based on a prior estimate. Copyright © 2015 John Wiley & Sons, Ltd.

]]>In this paper, we compared two different methods, one numerical technique, viz Legendre multiwavelet method, and the other analytical technique, viz optimal homotopy asymptotic method (OHAM), for solving fractional-order Kaup–Kupershmidt (KK) equation. Two-dimensional Legendre multiwavelet expansion together with operational matrices of fractional integration and derivative of wavelet functions is used to compute the numerical solution of nonlinear time-fractional KK equation. The approximate solutions of time fractional Kaup–Kupershmidt equation thus obtained by Legendre multiwavelet method are compared with the exact solutions as well as with OHAM. The present numerical scheme is quite simple, effective, and expedient for obtaining numerical solution of fractional KK equation in comparison to analytical approach of OHAM. Copyright © 2015 John Wiley & Sons, Ltd.

]]>A discontinuous Galerkin (DG) finite-element interior calculus is used as a common framework to describe various DG approximation methods for second-order elliptic problems. Using the framework, symmetric interior-penalty methods, local discontinuous Galerkin methods, and dual-wind discontinuous Galerkin methods will be compared by expressing all of the methods in primal form. The penalty-free nature of the dual-wind discontinuous Galerkin method will be both motivated and used to better understand the analytic properties of the various DG methods. Consideration will be given to Neumann boundary conditions with numerical experiments that support the theoretical results. Many norm equivalencies will be derived laying the foundation for applying dual-winding techniques to other problems. Copyright © 2015 John Wiley & Sons, Ltd.

]]>It is well known that a spherically symmetric wave speed problem in a bounded spherical region may be reduced, by means of Liouville transform, to the Sturm–Liouville problem *L*(*q*) in a finite interval. In this work, a uniqueness theorem for the potential *q* of the derived Sturm–Liouville problem *L*(*q*) is proved when the data are partial knowledge of the given spectra and the potential. Copyright © 2015 John Wiley & Sons, Ltd.

W. Sprößig In this paper, we propose a new adaptive method for frequency-domain identification problem of discrete LTI systems. It is based on a dictionary that is consisting of normalized reproducing kernels. We prove that the singular values of the matrix generated by this dictionary converge to zero rapidly; this makes it quite efficient in representing the original systems with only a few elements. For different systems, it results in different selected sequences from the dictionary, that is, its adaptivity. Meanwhile, the stability of results is automatically guaranteed according to the structure of the dictionary. Two examples are presented to illustrate the idea. Copyright © 2015 John Wiley & Sons, Ltd.

]]>In this paper, a new numerical method for solving the fractional Bagley-Torvik equation is presented. The method is based upon hybrid functions approximation. The properties of hybrid functions consisting of block-pulse functions and Bernoulli polynomials are presented. The Riemann-Liouville fractional integral operator for hybrid functions is introduced. This operator is then utilized to reduce the solution of the initial and boundary value problems for the fractional Bagley-Torvik differential equation to a system of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the technique. Copyright © 2015 John Wiley & Sons, Ltd.

]]>We consider the Cauchy problem for the Vlasov–Maxwell–Fokker–Planck system in the plane. It is shown that for smooth initial data, as long as the electromagnetic fields remain bounded, then their derivatives do also. Glassey and Strauss have shown this to hold for the relativistic Vlasov–Maxwell system in three dimensions, but the method here is totally different. In the work of Glassey and Strauss, the relativistic nature of the particle transport played an essential role. In this work, the transport is nonrelativistic, and smoothing from the Fokker–Planck operator is exploited. Copyright © 2015 John Wiley & Sons, Ltd.

]]>We establish a new regularity criterion for the 2D full compressible magnetohydrodynamic system in a bounded domain. Copyright © 2014 John Wiley & Sons, Ltd.

]]>This work deals with a mathematical model of an age-cycle length structured cell population. Each cell is distinguished by its age and its cycle length. The cellular mitosis is mathematically described by non-compact boundary conditions. We prove then that this mathematical model is governed by a positive *C*_{0}-semigroup. Copyright © 2014 John Wiley & Sons, Ltd.

In this study, we investigate the existence of mild solutions for a class of impulsive neutral stochastic integro-differential equations with infinite delays, using the Krasnoselskii–Schaefer type fixed point theorem combined with theories of resolvent operators. As an application, an example is provided to illustrate the obtained result. Copyright © 2014 John Wiley & Sons, Ltd.

]]>In this paper, we consider the non-Lipschitz stochastic differential equations and stochastic functional differential equations with delays driven by Lévy noise, and the approximation theorems for the solutions to these two kinds of equations will be proposed respectively. Non-Lipschitz condition is much weaker condition than the Lipschitz one. The simplified equations will be defined to make its solutions converge to that of the corresponding original equations both in the sense of mean square and probability, which constitute the approximation theorems. Copyright © 2014 John Wiley & Sons, Ltd.

In this article, we are concerned with the interactions of delta shock waves with contact discontinuities for the relativistic Euler equations for Chaplygin gas by using split delta functions method. The solutions are obtained constructively and globally when the initial data consists of three piecewise constant states. The global structure and large time-asymptotic behaviors of the solutions are analyzed case by case. During the process of the interaction, the strengths of delta shock waves are computed completely. Moreover, it can be found that the Riemann solutions are stable for such small perturbations with special initial data by letting perturbed parameter *ε* tends to zero. Copyright © 2014 John Wiley & Sons, Ltd.

In the paper, we investigate the basic transmission problems arising in the model of fluid-solid acoustic interaction when a piezo-ceramic elastic body ( Ω^{ + }) is embedded in an unbounded fluid domain ( Ω^{ − }). The corresponding physical process is described by boundary-transmission problems for second order partial differential equations. In particular, in the bounded domain Ω^{ + }, we have 4 × 4 dimensional matrix strongly elliptic second order partial differential equation, while in the unbounded complement domain Ω^{ − }, we have a scalar Helmholtz equation describing acoustic wave propagation. The physical kinematic and dynamic relations mathematically are described by appropriate boundary and transmission conditions. With the help of the potential method and theory of pseudodifferential equations, the uniqueness and existence theorems are proved in Sobolev–Slobodetskii spaces. Copyright © 2014 John Wiley & Sons, Ltd.

In this article, we prove the existence of solutions to the coagulation equation with singular kernels. We use weighted *L*^{1}-spaces to deal with the singularities in order to obtain regular solutions. The Smoluchowski kernel is covered by our proof. The weak *L*^{1} compactness methods are applied to suitably chosen approximating equations as a base of our proof. A more restrictive uniqueness result is also mentioned. Copyright © 2014 John Wiley & Sons, Ltd.

We consider standing waves for 4-superlinear Schrödinger–Kirchhoff equations in with potential indefinite in sign. The nonlinearity considered in this study satisfies a condition that is much weaker than the classical Ambrosetti–Rabinowitz condition. We obtain a nontrivial solution and, in the case of odd nonlinearity, an unbounded sequence of solutions via the Morse theory and the fountain theorem, respectively. Copyright © 2014 John Wiley & Sons, Ltd.

]]>In this paper, we present a collection of *a priori* estimates of the electromagnetic field scattered by a general bounded domain. The constitutive relations of the scatterer are in general anisotropic. Surface averages are investigated, and several results on the decay of these averages are presented. The norm of the exterior Calderón operator for a sphere is investigated and depicted as a function of the frequency. Copyright © 2014 John Wiley & Sons, Ltd.

In this paper, the exponential synchronization problem of delayed coupled reaction-diffusion systems on networks (DCRDSNs) is investigated. Based on graph theory, a systematic method is designed to achieve exponential synchronization between two DCRDSNs by constructing a global Lyapunov function for error system. Two different kinds of sufficient synchronization criteria are derived in the form of Lyapunov functions and coefficients of drive-response systems, respectively. Finally, a numerical example is given to show the usefulness of the proposed criteria. Copyright © 2014 John Wiley & Sons, Ltd.

]]>In this paper, we investigate the existence and multiplicity of solutions to the following second-order impulsive Hamiltonian systems:

where is a continuousmap form the interval [0, *T*] to the set of N-order symmetric matrices. Our methods are based on critical point theory for nondifferentiable functionals. Copyright © 2014 John Wiley & Sons, Ltd.

In this paper, we investigate the computability of the solution operator of the generalized KdV-Burgers equation with initial-boundary value problem. Here, the solution operator is a nonlinear map *H*^{3m − 1}(*R*^{+}) × *H*^{m}(0,*T*)*C*([0,*T*];*H*^{3m − 1}(*R*^{+})) from the initial-boundary value data to the solution of the equation. By a technique that is widely used for the study of nonlinear dispersive equation, and using the type 2 theory of effectivity as computable model, we prove that the solution map is Turing computable, for any integer *m* ≥ 2, and computable real number *T* > 0. Copyright © 2014 John Wiley & Sons, Ltd.

This paper is concerned with the controllability and stabilizability problem for control systems described by a time-varying linear abstract differential equation with distributed delay in the state variables. An approximate controllability property is established, and for periodic systems, the stabilization problem is studied. Assuming that the semigroup of operators associated with the uncontrolled and non delayed equation is compact, and using the characterization of the asymptotic stability in terms of the spectrum of the monodromy operator of the uncontrolled system, it is shown that the approximate controllability property is a sufficient condition for the existence of a periodic feedback control law that stabilizes the system. The result is extended to include some systems which are asymptotically periodic. Copyright © 2014 John Wiley & Sons, Ltd.

]]>In the present study, we propose and analyze a predator–prey system with disease in the predator population. To understand the role of cannibalism, we modify the model considering predator population is of cannibalistic type. Local and global stability around the biologically feasible equilibria are studied. The conditions for the persistence of the system are worked out. We also analyze and compare the community structure of the model systems with the help of ecological and disease basic reproduction numbers. Finally, through numerical simulation, we observe that inclusion of cannibalism in predator population may control the disease transmission in the susceptible predator population. Copyright © 2014 John Wiley & Sons, Ltd.

]]>In this paper, we constructed the split-step *θ *(SS*θ*)-method for stochastic age-dependent population equations. The main aim of this paper is to investigate the convergence of the SS *θ*-method for stochastic age-dependent population equations. It is proved that the proposed method is convergent with strong order 1/2 under given conditions. Finally, an example is simulated to verify the results obtained from the theory, and comparative analysis with Euler method is given, the results show the higher accuracy of the SS *θ*-method. Copyright © 2014 John Wiley & Sons, Ltd.

On the basis of zero curvature equations from semi-direct sums of Lie algebras, we construct integrable couplings of the Giachetti–Johnson hierarchy of soliton equations. We also establish Hamiltonian structures of the resulting integrable couplings by the variational identity. Moreover, we obtain bi-integrable couplings of the Giachetti–Johnson hierarchy and their Hamiltonian structures by applying a class of non-semisimple matrix loop algebras consisting of triangular block matrices. Copyright © 2014 John Wiley & Sons, Ltd.

]]>This paper revisits and complement in different directions the classical work by W. T. Reid on symmetrizable completely continuous transformations in Hilbert spaces and a more recent paper by one of the authors. More precisely, we deal with spectral properties of *% non-compact* operators *G* on a complex Hilbert space *H* such that *SG* is self-adjoint where *S* is a (*not* necessarily injective) nonnegative operator. We study the isolated eigenvalues of *G* outside its essential spectral interval and provide variational characterization of them as well as stability estimates. We compare them also to spectral objects of *S**G*. Finally, we characterize the Schechter essential spectrum of strongly symmetrizable operators in terms singular Weyl sequences; in particular, we complement J. I. Nieto's paper on the essential spectrum of symmetrizable. Copyright © 2014 John Wiley & Sons, Ltd.

In this paper, we are interested in looking for multiple solutions for the following system of nonhomogenous Kirchhoff-type equations:

- (1.1)

where constants *a*,*c* > 0;*b*,*d*,*λ*≥0, *N* = 1,2 or 3, *f*,*g*∈*L*^{2}(*R*^{N}) and *f*,*g*≢0, *F*∈*C*^{1}(*R*^{N}×*R*^{2},*R*), , *V*∈*C*(*R*^{N},*R*) satisfy some appropriate conditions. Under more relaxed assumptions on the nonlinear term *F*, the existence of one negative energy solution and one positive energy solution for the nonhomogenous system 2.1 is obtained by Ekeland's variational principle and Mountain Pass Theorem, respectively. Copyright © 2014 John Wiley & Sons, Ltd.

We consider a weakly dissipative modified two-component Dullin–Gottwald–Holm system. The existence of global weak solutions to the system is established. We first give the well-posedness result of viscous approximate problem and obtain the basic energy estimates. Then, we show that the limit of the viscous approximation solutions is a global weak solution to the system. Copyright © 2014 John Wiley & Sons, Ltd.

]]>In this paper, we employed the bifurcation method and qualitative theory of dynamical systems to study the peakons and periodic cusp waves of the generalization of the Camassa-Holm equation, which may be viewed as an extension of peaked waves of the same equation. Through the bifurcation phase portraits of traveling wave system, we obtained the explicit peakons and periodic cusp wave solutions. Further, we exploited the numerical simulation to confirmthe qualitative analysis, and indeed, the simulation results are in accord with the qualitative analysis. Compared with the previous works, several new nonlinear wave solutions are obtained. Copyright © 2014 John Wiley & Sons, Ltd.

]]>The weighted *L*^{r}-asymptotic behavior of the strong solution and its first-order spacial derivatives to the incompressible magnetohydrodynamic (MHD) equations is established in a half-space. Further, the *L*^{∞}-decay rates of the second-order spatial derivatives of the strong solution are derived by using the Stokes solution formula and employing a decomposition for the nonlinear terms in MHD equations. Copyright © 2014 John Wiley & Sons, Ltd.

In this paper, we consider a one-dimensional linear Bresse system with infinite memories acting in the three equations of the system. We establish well-posedness and asymptotic stability results for the system under some conditions imposed into the relaxation functions regardless to the speeds of wave propagations. Copyright © 2014 John Wiley & Sons, Ltd.

]]>This paper is devoted to the investigation of the global dynamics of a SEIR model with information dependent vaccination. The basic reproduction number is derived for the model, and it is shown that gives the threshold dynamics in the sense that the disease-free equilibrium is globally asymptotically stable and the disease dies out if , while there exists at least one positive periodic solution and the disease is uniformly persistent when . Further, we give the approximation formula of . This answers the concerns presented in [B. Buonomo, A. d'Onofrio, D. Lacitignola, Modeling of pseudo-rational exemption to vaccination for SEIR diseases, J. Math. Anal. Appl. 404 (2013) 385–398]. Copyright © 2014 John Wiley & Sons, Ltd.

]]>In this paper, the Darboux transformation of the Kundu–nonlinear Schrödinger equation is derived and generalized to the matrix of *n*-fold Darboux transformation. From known solution *Q*, the determinant representation of *n*-th new solutions of *Q*^{[n]} are obtained by the *n*-fold Darboux transformation. Then soliton solutions and positon solutions are generated from trivial seed solutions, breather solutions and rogue wave solutions that are obtained from periodic seed solutions. After that, the higher order rogue wave solutions of the Kundu–nonlinear Schrödinger equation are given. We show that free parameters in eigenfunctions can adjust the patterns of the higher order rogue waves. Meanwhile, the third-order rogue waves are given explicitly. Copyright © 2014 John Wiley & Sons, Ltd.