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In this paper, the authors give sufficient conditions for the boundedness and global asymptotic stability of solutions to certain nonlinear multi-delay functional differential equations of the third order. The technique of proof involves defining an appropriate Lyapunov-Krasovskii functional and applying LaSalle's invariance principle. An example is included to illustrate the results. Copyright (C) 2014 JohnWiley & Sons, Ltd.

In this paper, we consider a three dimensional quantum Navier-Stokes-Poisson equations. Existence of global weak solutions is obtained, and convergence toward the classical solution of the incompressible Navier-Stokes equation is rigorously proven for well prepared initial data. Furthermore, the associated convergence rates are also obtained. Copyright © 2014 John Wiley & Sons, Ltd.

In this paper, the stability problem of impulsive functional differential equations with infinite delays is considered. By using Lyapunov functions and the Razumikhin technique, some new theorems on the uniform stability and uniform asymptotic stability are obtained. The obtained results are milder and more general than several recent works. Two examples are given to demonstrate the advantages of the results. Copyright © 2014 John Wiley & Sons, Ltd.

In this paper, we prove the existence and uniqueness of a solution for a class of backward stochastic differential equations driven by G-Brownian motion with subdifferential operator by means of the Moreau–Yosida approximation method. Moreover, we give a probabilistic interpretation for the viscosity solutions of a kind of nonlinear variational inequalities. Copyright © 2017 John Wiley & Sons, Ltd.

In this paper, we are concerned with the existence of ground state solution for the following fractional differential equations with tempered fractional derivative: D−α,λ(D+α,λu(t))=f(t,u(t)),t∈Ru∈Wα,2(R),(FD) where α∈(1/2,1), λ>0, D±α,λu are the left and right tempered fractional derivatives, Wα,2(R) is the fractional Sobolev spaces, and f∈C(R×R,R). Assuming that f satisfies the Ambrosetti–Rabinowitz condition and another suitable conditions, by using mountain pass theorem and minimization argument over Nehari manifold, we show that (FD) has a ground state solution. Furthermore, we show that this solution is a radially symmetric solution. Copyright © 2017 John Wiley & Sons, Ltd.

In this paper, we consider the shape inverse problem of a body immersed in the incompressible fluid governed by thermodynamic equations. By applying the domain derivative method, we obtain the explicit representation of the derivative of solution with respect to the boundary, which plays an important role in the inverse design framework. Moreover, according to the boundary parametrization technique, we present a regularized Gauss–Newton algorithm for the shape reconstruction problem. Finally, numerical examples indicate the proposed algorithm is feasible and effective for the low Reynolds numbers. Copyright © 2017 John Wiley & Sons, Ltd.

We prove the existence of weak solutions to a one-dimensional initial-boundary value problem for a model system of partial differential equations, which consists of a sub-system of linear elasticity and a nonlinear non-uniformly parabolic equation of second order. To simplify the existence proof of weak solutions in the 2006 paper of Alber and Zhu, we replace the function |p|κ:=|p|2/|p|2+κ2 in that work by |p|κ:=|p|2+κ2. The model is formulated by using a sharp interface model for phase transformations that are driven by material forces. Copyright © 2017 John Wiley & Sons, Ltd.

This paper is devoted to study the periodic nature of the solution of the following max-type difference equation: where the initial conditions x−2,x−1,x0 are arbitrary positive real numbers and is a periodic sequence of period two. Copyright © 2014 John Wiley & Sons, Ltd.

In this paper, we study an optimal control problem for the mixed boundary value problem for an elastic body with quasistatic evolution of an internal damage variable. We suppose that the evolution of microscopic cracks and cavities responsible for the damage is described by a nonlinear parabolic equation. A density of surface traction p acting on a part of boundary of an elastic body Ω is taken as a boundary control. Because the initial boundary value problem of this type can exhibit the Lavrentieff phenomenon and non-uniqueness of weak solutions, we deal with the solvability of this problem in the class of weak variational solutions. Using the convergence concept in variable spaces and following the direct method in calculus of variations, we prove the existence of optimal and approximate solutions to the optimal control problem under rather general assumptions on the quasistatic evolution of damage. Copyright © 2014 John Wiley & Sons, Ltd.

This paper is devoted to the study of a nonlinear parabolic p(x)-Laplace equation with gradient term and L1 data. The authors obtain the existence of renormalized solutions via strong convergence of truncation. Copyright © 2014 John Wiley & Sons, Ltd.

In this paper, a collocation method is given to solve singularly perturbated two-point boundary value problems. By using the collocation points, matrix operations and the matrix relations of the Bessel functions of the first kind and their derivatives, the boundary value problem is converted to a system of the matrix equations. By solving this system, the approximate solution is obtained. Also, an error problem is constructed by the residual function, and it is solved by the presented method. Thus, the error function is estimated, and the approximate solutions are improved. Finally, numerical examples are given to show the applicability of the method, and also, our results are compared by existing results. Copyright © 2014 JohnWiley & Sons, Ltd.

The short-time Fourier transform has been shown to be a powerful tool for non-stationary signals and time-varying systems. This paper investigates the signal moments in the Hardy–Sobolev space that do not usually have classical derivatives. That is, signal moments become valid for non-smooth signals if we replace the classical derivatives by the Hardy–Sobolev derivatives. Our work is based on the extension of Cohen's contributions to the local and global behaviors of the signal. The relationship of the moments and spreads of the signal in the time, frequency and short-time Fourier domain are established in the Hardy–Sobolev space. Copyright © 2014 John Wiley & Sons, Ltd.

In this paper, sufficient conditions are established for the existence and uniqueness of global solutions to stochastic impulsive systems with expectations in the nonlinear terms. The maximal interval and the estimate of mild solutions are also discussed. These results are obtained by using the fixed point theorem, interval partition, and Lyapunov-like technique. Finally, examples are given to illustrate the theory. Copyright © 2014 John Wiley & Sons, Ltd.

Solvability of Cauchy's problem in for fractional Hamilton–Jacobi equation (1.1) with subcritical nonlinearity is studied here both in the classical Sobolev spaces and in the locally uniform spaces. The first part of the paper is devoted to the global in time solvability of subcritical equation (1.1) in locally uniform phase space, a generalization of the standard Sobolev spaces. Subcritical growth of the nonlinear term with respect to the gradient is considered. We prove next the global in time solvability in classical Sobolev spaces, in Hilbert case. Regularization effect is used there to guarantee global in time extendibility of the local solution. Copyright © 2014 John Wiley & Sons, Ltd.

In this paper, we consider a discrete fractional boundary value problem of the form: where 0 0, , is a continuous function, and Eβx(t) = x(t + β − 1). The existence and uniqueness of solutions are proved by using Banach's fixed point theorem. An illustrative example is also presented. Copyright © 2014 John Wiley & Sons, Ltd.

In this paper, we are concerned with the Cauchy problem for the density-dependent incompressible flow of liquid crystals in thewhole space (N ≥ 2).We prove the localwell-posedness for large initial velocity field and director field of the system in critical Besov spaces if the initial density is close to a positive constant. We show also the global well-posedness for this system under a smallness assumption on initial data. In particular, this result allows us to work in Besov space with negative regularity indices, where the initial velocity becomes small in the presence of the strong oscillations. Copyright © 2014 John Wiley & Sons, Ltd.

In this paper, we study the existence of solutions with prescribed L-2-norm for the following Kirchhoff type equation: -(a + b integral(RN) vertical bar del u vertical bar(2))Delta u -vertical bar u vertical bar(p-2)u =lambda u, x is an element of R-N, lambda is an element of R, where N 0 are constants, p is an element of(2, 2*), 2 = 6 if N = 3, and 2*= +infinity if N = 1, 2. We obtain the sharp existence of global constraint minimizers for 2 < p

In this paper we construct two distinct generalized holomorphic orthogonal function systems over infinite cylinders in . Explicit representation formulae and properties of the obtained basis functions are given. As an application, we present some plot simulations that illustrate the results of this work. Copyright © 2014 John Wiley & Sons, Ltd.

This paper is concerned with asymptotic stability of a Bresse system with two frictional dissipations. Under mathematical condition of equal speed of wave propagation, we prove that the system is exponentially stable. Otherwise, we show that Bresse system is not exponentially stable. Then, in the latter case, by using a recent result in linear operator theory, we prove the solution decays polynomially to zero with optimal decay rate. Better rates of polynomial decay depending on the regularity of initial data are also achieved. 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∈L2(RN) and f,g≢0, F∈C1(RN×R2,R), , V∈C(RN,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.

This paper considers the one parameter families of extrinsic differential geometries of Lorentzian hypersurfaces on pseudo n-spheres. We give a continuous relationship among the three types Gauss indicatrices by one parameter map. Meanwhile, we also give the singularity analysis of the one parameter Gauss indicatrices of Lorentzian hypersurfaces on pseudo n-spheres by the Legendrian singularity theory. Copyright © 2014 John Wiley & Sons, Ltd.

This paper deals with a fully parabolic attraction–repulsion chemotaxis system in two-dimensional smoothly bounded domains. It is shown that the system admits global bounded classical solutions whenever the repulsion is dominated. The proof is based on an entropy-like inequality and coupled estimate techniques. 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.

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, the Darboux transformation of the Kundu–nonlinear Schrodinger 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 Schrodinger 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.

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 C / � H m .0,T/ ! C.Œ0,T� ;H 3m� 1 .R C //, 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 integerm � 2, and computable real numberT > 0. 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 Calderon operator for a sphere is investigated and depicted as a function of the frequency.

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 paper, we prove the -boundedness of solution operator families of the generalized Stokes resolvent problem in an infinite layer with resolvent parameter , where , and our boundary conditions are nonhomogeneous Neumann on upper boundary and Dirichlet on lower boundary. We want to emphasize that we can choose 0 0 arbitrarily, although usual parabolic theorem tells us that we must choose a large γ0 > 0 for given 0

In this paper, we consider the non-Lipschitz stochastic differential equations and stochastic functional differential equations with delays driven by Levy 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.

This paper describes well-posedness, spectral representations, and approximations of solutions of uniformly elliptic, second-order, divergence form elliptic boundary value problems on exterior regions U in when N ≥ 3. Inhomogeneous Dirichlet, Neumann, and Robin boundary conditions are treated. These problems are first shown to be well-posed in the space E1(U) of finite-energy functions on U using variational methods. Spectral representations of these solutions involving Steklov eigenfunctions and solutions subject to zero Dirichlet boundary conditions are described. Some approximation results for the A-harmonic components are obtained. Positivity and comparison results for these solutions are given. Copyright © 2014 John Wiley & Sons, Ltd.

The paper presents a study of propagation of shear wave (SH-wave) in an orthotropic elastic medium under initial stress sandwiched by a homogeneous semi-infinite medium and an inhomogeneous half-space. The technique of separation of variables has been adopted to get the analytical solutions for the dispersion relation in a closed form. The propagation of SH-waves is influenced by inhomogeneity parameters and initial stress parameter. Velocities of SH-waves are calculated numerically for different cases. As a special case when the intermediate layer and half-space are homogeneous, computed frequency equation coincides with general equation of Love wave. To study the effect of inhomogeneity parameters and initial stress parameter, we have plotted the velocity of SH-wave in several figures and observed that the velocity of wave decreases with the increases of non-dimensional wave number. It can be found that the phase velocity decreases with the increase of inhomogeneity parameters. We observed that the velocity of SH-wave decreases with the increases of initial stress parameter in both homogeneous and inhomogeneous media. GUI has been developed by using MATLAB to generalize the effect of the parameters discussed. Copyright © 2014 John Wiley & Sons, Ltd.

We study bifurcations from radial solution of a free boundary problem modeling the dormant state of nonnecrotic solid tumors in the presence of external inhibitors. This problem consists in three linear elliptic equations with two Dirichlet and one Neumann boundary conditions and a fourth boundary condition coupling surface tension effects on free boundary. In this paper, surface tension coefficient γ plays the role of bifurcation parameter. We prove that in certain situations there exists a positive null point sequence for γ where bifurcation occurs from radial solution, while in the other situations, either bifurcation occurs at only finite many points of γ or even it does not occur for any γ > 0. Copyright © 2014 John Wiley & Sons, Ltd.

The bound of a chaotic system is important for chaos control, chaos synchronization, and other applications. In the present paper, the bounds of the generalized Lorenz system are studied, based on the Lyapunov function theory and the Lagrange multiplier method. We obtain a precise bound for the generalized Lorenz system. The rate of the trajectories is also obtained. Furthermore, we perform the numerical simulations. Numerical simulations are presented to show the effectiveness of the proposed scheme. Copyright © 2014 John Wiley & Sons, Ltd.

In this paper, we study the following modified Kirchhoff-type equations of the form: where a > 0, b ≥ 0, and . Under appropriate assumptions on V (x) and h(x,u), some existence results for positive solutions, negative solutions, and sequence of high energy solutions are obtained via a perturbation method. Copyright © 2014 John Wiley & Sons, Ltd.

In this paper, we present some existence results on L1 spaces of a nonlinear boundary value problem derived from a model introduced by Rotenberg (1983) describing the growth of a cell population. Each cell of this population is distinguished by its degree of maturity μ ∈ [0,1] and its maturation velocity v. The biological boundary at μ = 0 and μ = 1 are fixed and tightly coupled through the mitosis. At mitosis, daughter cells and mother cells are related by a general reproduction rule, which covers all known biological ones. In this work, the maturation velocity is allowed to be infinite, that is, v ∈ [0, + ∞ ). This hypothesis introduce some mathematical difficulties, which are overcomed by using a measure of weak noncompactness adapted to the problem and a recent fixed point theorem (Theorem 3.2) involving weakly compact operators on nonreflexive Banach spaces. Copyright © 2014 John Wiley & Sons, Ltd.

In this paper, we develop a continuation principle for general hyperbolic singular limit problems in more general Besov spaces, which covers the cases of usual Sobolev spaces with higher regularity in and the critical Besov space. As an application, we give a simple justification for the low Mach number limit of compressible magnetohydrodynamics equations. More precisely, for the Mach number sufficiently small, the smooth compressible flows exist on the (finite) time interval where the incompressible magnetohydrodynamics equations have smooth solutions, and the definite convergence orders are also obtained. Copyright © 2014 John Wiley & Sons, Ltd.

In this paper, by using the Nehari manifold approach in combination with periodic approximations, we obtain the sufficient conditions on the existence of the nontrivial ground state solutions of the periodic discrete coupled nonlinear Schrodinger equations. Copyright © 2014 John Wiley & Sons, Ltd.

Dimension functions play a significant role in the study of wavelets and have been attracting many waveletters’ interest. In recent years, the study of wavelet dimension functions has seen great achievements, but the study of Parseval frame wavelet (PFW) dimension functions has not. Bownik, Rzeszotnik and Speegle in 2001 and Arambasic, Bakic and Rajic in 2007 characterized -periodic functions that are wavelet dimension functions. But it is open what a -periodic function is qualified to be a dimension function of some semi-orthogonal PFW. This paper addresses semi-orthogonal PFW dimension functions associated with expansive matrices of determinant ± 2. We obtain a description of the ranges of semi-orthogonal PFW dimension functions and establish a necessary and sufficient condition for an integer-valued function to be a dimension function of some semi-orthogonal PFW. Copyright © 2014 John Wiley & Sons, Ltd.

In this paper, we give positive answer to the open question raised in [E. Zuazua, Exponential decay for the semilinear wave equation with localized damping in unbounded domains. J. Math. Pures Appl., 70 (1991) 513--529] on the exponential decay of solutions for the semilinear plate equation with localized damping., 16 pages

In this paper, we consider a class of second-order initial value problems. We extend the family of second-order initial value problems for which the existence and uniqueness of a solution is known. To handle the singularity, we introduce the more general Caratheodory type of restrictions. The solvability results of the Emden–Fowler type of equations is established as a special case.Copyright © 2014 John Wiley & Sons, Ltd.

This paper is concerned with a class of dynamic boundary systems with boundary feedback. The well-posedness of the considered systems is proved under some regularity conditions. Moreover, some spectral properties are derived. As an application, the well-posedness and the asymptotic behavior of population dynamical systems with unbounded birth process ‘ ’ are solved. Such population dynamical systems were pointed out in [S. Piazzera, Math. Methods Appl. Sci., 27 (2004), 427-439] to be a current research topic in semigroup theory and still an open problem. Copyright © 2014 John Wiley & Sons, Ltd.

This paper is concerned with the simple waves for the general quasilinear strictly hyperbolic systems in two independent variables. By using the method of characteristic decomposition, we first establish a more general sufficient condition for the existence of characteristic decompositions. These decompositions allow us to extend a well-known result on reducible equations by Courant and Friedrichs to the non-reducible equations. Then we construct a simple wave solution, in which the characteristics may be a set of non-straight curves, around a given curve under the obtained sufficient condition. Copyright © 2014 John Wiley & Sons, Ltd.

In this paper we study a Large Eddy Simulation (LES) model for the approximation of large scales of the 3D Boussinesq equations. This model is obtained using the approach first described by Stolz and Adams, based on the Van Cittern approximate deconvolution operators, and applied to the filtered Boussinesq equations. Existence and uniqueness of a regular weak solution are provided. Our main objective is to prove that this solution converges towards a solution of the filtered Boussinesq equations, as the deconvolution parameter goes to zero.

In this paper, we will obtain that there exists a maximizer for the non-endpoint Strichartz inequalities for the fourth-order Schrodinger equation with initial data in the L2(Rd) space in all dimensions, and then we obtain a maximizer also for the non-endpoint Sobolev–Strichartz inequality for the fourth-order Schrodinger equation with initial data in the homogeneous Sobolev space. Our analysis derived from the linear profile decomposition. Copyright © 2014 John Wiley & Sons, Ltd.

In this paper, the analytical approximate traveling wave solutions of Whitham–Broer–Kaup (WBK) equations, which contain blow-up solutions and periodic solutions, have been obtained by using the coupled fractional reduced differential transform method. By using this method, the solutions were calculated in the form of a generalized Taylor series with easily computable components. The convergence of the method as applied to the WBK equations is illustrated numerically as well as analytically. By using the present method, we can solve many linear and nonlinear coupled fractional differential equations. The results justify that the proposed method is also very efficient, effective and simple for obtaining approximate solutions of fractional coupled modified Boussinesq and fractional approximate long wave equations. Numerical solutions are presented graphically to show the reliability and efficiency of the method. Moreover, the results are compared with those obtained by the Adomian decomposition method (ADM) and variational iteration method (VIM), revealing that the present method is superior to others. Copyright © 2014 John Wiley & Sons, Ltd.

This paper deals with the Cauchy problem for a doubly degenerate parabolic equation with variable coefficient For the case λ + 1 ≥ N, one proves that depending on the behavior of the variable coefficient at infinity, the Cauchy problem either possesses the property of finite speed of propagation of perturbation or the support blows up in finite time. This completes a result by Tedeev (A.F.Tedeev, The interface blow-up phenomenon and local estimates for doubly degenerate parabolic equations, Appl. Anal. 86 (2007) 755–782.), which asserts the same result under the condition λ + 1

In this paper, we consider an inverse source problem of identification of F(t) function in the linear parabolic equation ut = uxx + F(t) and u0(x) function as the initial condition from the measured final data and local boundary data. Based on the optimal control framework by Green's function, we construct Frechet derivative of Tikhonov functional. The stability of the minimizer is established from the necessary condition. The CG algorithm based on the Frechet derivative is applied to the inverse problem, and results are presented for a test example. Copyright © 2014 John Wiley & Sons, Ltd.

In this paper, we study the existence of multiple positive solutions for a degenerate nonlocal problem on unbounded domain. Using the Ekeland's variational principle combined with the mountain pass theorem, we show that problem admits at least two positive solutions under several different conditions. Copyright © 2014 John Wiley & Sons, Ltd.

In this paper, we investigate a class of delay Nicholson's blowflies model with a linear harvesting term, new criteria for the existence and convergence dynamics of positive pseudo almost periodic solutions are established by using the fixed point method and the properties of pseudo almost periodic function, together with constructing suitable Lyapunov functionals. The obtained results extend previously known results, and they also partially answer an open problem proposed by L. Berezansky et al. Finally, an example with simulation is presented to demonstrate the effectiveness of theoretical results. Copyright © 2014 John Wiley & Sons, Ltd.