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This paper is focused on following time-harmonic Maxwell equation: ∇×(μ−1(x)∇×u)−ω2e(x)u=f(x,u),inΩ,ν×u=0,on∂Ω, where Ω⊂R3 is a bounded Lipschitz domain, ν:∂Ω→R3 is the exterior normal, and ω is the frequency. The boundary condition holds when Ω is surrounded by a perfect conductor. Assuming that f is asymptotically linear as |u|→∞, we study the above equation by improving the generalized Nehari manifold method. For an anisotropic material with magnetic permeability tensor μ∈R3×3 and permittivity tensor e∈R3×3, ground state solutions are established in this paper. Applying the principle of symmetric criticality, we find 2 types of solutions with cylindrical symmetries in particular for the uniaxial material.

This paper deals with an adaptation of the Poincare-Lindstedt method for the determination of periodic orbits in three-dimensional nonlinear differential systems. We describe here a general symbolic algorithm to implement the method and apply it to compute periodic solutions in a three-dimensional Lotka-Volterra system modeling a chain food interaction. The sufficient conditions to make secular terms disappear from the approximate series solution are given in the paper.

This paper addresses a study of the controllability for a class of heat equations with memory in one spacial dimension. Unlike the classical heat equation, a heat equation with memory in general is not null controllable. There always exists a set of initial values such that the property of the null controllability fails. Also, one does not know whether there are nontrivial initial values, which can be driven to zero with a boundary control. In this paper, we give a characterization of the set of such nontrivial initial values. On the other hand, if a moving control is imposed on this system with memory, we prove the null controllability of it in a suitable state space for any initial value. Copyright © 2016 John Wiley & Sons, Ltd.

In this paper, we are interested in a model derived from the 1-D Keller-Segel model on the half line x > as follows: ut−lux−uxx=−β(uvx)x,x>0,t>0,λv−vxx=u,x>0,t>0,lu(0,t)+ux(0,t)=vx(0,t)=0,t>0,u(x,0)=u0(x),x>0, where l is a constant. Under the conserved boundary condition, we study the asymptotic behavior of solutions. We prove that the problem is always globally and classically solvable when the initial data is small, and moreover, we obtain the decay rates of solutions. The paper mainly deals with the case of l > 0. In this case, the solution to the problem tends to a conserved stationary solution in an exponential decay rate, which is a very different result from the case of l

This paper applies Nevanlinna theory of value distribution to discuss existence of solutions of certain types of non-linear differential-difference equations such as (5) and (8) given in the succeeding paragraphs. Existence of solutions of differential equations and difference equations can be said to have been well studied, that of differential-difference equations, on the other hand, have been paid little attention. Such mixed type equations have great significance in applications. This paper, in particular, generalizes the Rellich–Wittich-type theorem and Malmquist-type theorem about differential equations to the case of differential-difference equations. Copyright © 2015 John Wiley & Sons, Ltd.

In this paper, we constructed the split-step θ (SSθ)-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.

In a recent paper, the authors have introduced the windowed linear canonical transform and shown its good properties together with some applications such as Poisson summation formulas, sampling interpolation, and series expansion. In this paper, we prove the Paley–Wiener theorems and the uncertainty principles for the (inverse) windowed linear canonical transform. They are new in literature and has some consequences that are now under investigation. Copyright © 2012 John Wiley & Sons, Ltd.

This paper is focused on higher order differentiation of Fourier series of functions. By means of Stokes's transformation, the recursion relations between the Fourier coefficients in Fourier series of different order (partial) derivatives of the functions as well as the general formulas for Fourier series of higher order (partial) derivatives of the functions are acquired. And then, the sufficient conditions for term-by-term differentiation of Fourier series of the functions are presented. These findings are subsequently used to reinvestigate the Fourier series methods for linear elasto-dynamical systems. The results given in this paper on the constituent elements, together with their combinatorial modes and numbering, of the sets of coefficients concerning 2rth order linear differential equation with constant coefficients are found to be different from the results deduced by Chaudhuri back in 2002. And it is also shown that the displacement solution proposed by Li in 2009 is valid only when the second order mixed partial derivative of the displacement vanishes at all of the four corners of the rectangular plate. Copyright © 2016 John Wiley & Sons, Ltd.

The objective of this paper is to present an algorithm from which a rapidly convergent solution is obtained for Volterra integral equations of Hammerstein type. Such equations are often encountered when describing the response of viscoelastic materials where the time dependency of the material properties is often expressed in the form of a convolution integral. Frequently, singularity is encountered and often ignored when dealing with the constitutive equations of viscoelastic materials. In this paper, the singularity is incorporated in the solution and the iterative scheme used to solve the equation converges within six iterations to a typical toleration error of 10−5. The algorithm is applied to the strain response of a polymer under impulsive (constant) loading and the results show excellent correlation between the experimental and analytical solution. Copyright © 2010 John Wiley & Sons, Ltd.

This paper is concerned with computable and guaranteed upper bounds of the difference between exact solutions of variational inequalities arising in the theory of viscous fluids and arbitrary approximations in the corresponding energy space. Such estimates (also called error majorants of functional type) have been derived for the considered class of nonlinear boundary-value problems in (Math. Meth. Appl. Sci. 2006; 29:2225–2244) with the help of variational methods based on duality theory from convex analysis. In the present paper, it is shown that error majorants can be derived in a different way by certain transformations of the variational inequalities that define generalized solutions. The error bounds derived by this techniques for the velocity function differ from those obtained by the variational method. These estimates involve only global constants coming from Korn- and Friedrichs-type inequalities, which are not difficult to evaluate in case of Dirichlet boundary conditions. For the case of mixed boundary conditions, we also derive another form of the estimate that contains only one constant coming from the following assertion: the L2 norm of a vector-valued function from H1(Ω) in the factor space generated by the equivalence with respect to rigid motions is bounded by the L2 norm of the symmetric part of the gradient tensor. As for some ‘simple’ domains such as squares or cubes, the constants in this inequality can be found analytically (or numerically), we obtain a unified form of an error majorant for any domain that admits a decomposition into such subdomains. Copyright © 2009 John Wiley & Sons, Ltd.

This paper presents a semigroup approach for the mathematical analysis of the inverse coefficient problems of identifying the unknown coefficient k(ux) in the inhomogenenous quasi-linear parabolic equation ut(x, t)=(k(ux)ux(x, t))x +F(u), with the Dirichlet boundary conditions u(0, t)=ψ0, u(1, t)=ψ1 and source function F(u). The main purpose of this paper is to investigate the distinguishability of the input–output mappings Φ[·]:C1[0, T], Ψ[·]:C1[0, T] via semigroup theory. Copyright © 2009 John Wiley & Sons, Ltd.

In this paper, we present a recently developed mathematical model for short double-wall carbon nanotubes. The model is governed by a system of four hyperbolic equations representing the two Timoshenko beams coupled through the Van der Waals forces. The system is equipped with a four-parameter family of the boundary conditions and can be reduced to an evolution equation. This equation defines a strongly continuous semi-group. Spectral properties of the semi-group generator are presented in the paper. We show that it is an unbounded non-selfadjoint operator with compact resolvent. Moreover, this operator is a relatively compact perturbation of a certain selfadjoint operator. Copyright © 2008 John Wiley & Sons, Ltd.

In this paper, we present an analysis for the class of delay differential equations with one discrete delay and the right-hand side depending only on the past. We extend the results from paper by U. Foryś (Appl. Math. Lett. 2004; 17(5):581–584), where the right-hand side is a unimodal function. In the performed analysis, we state more general conditions for global stability of the positive steady state and propose some conditions for the stable Hopf bifurcation occurring when this steady state looses stability. We illustrate the analysis by biological examples coming from the population dynamics. Copyright © 2007 John Wiley & Sons, Ltd.

The present paper is concerned with an asymptotics of a solution to the model system of radiating gas. The previous researches have shown that the solution converges to a travelling wave with a rate (1 + t)−1/4 as time t tends to infinity provided that an initial data is given by a small perturbation from the travelling wave in the suitable Sobolev space and the perturbation is integrable. In this paper, we make more elaborate analysis under suitable assumptions on initial data in order to obtain shaper convergence rates than previous researches. The first result is that if the initial data decays at the spatial asymptotic point with a certain algebraic rate, then this rate reflects the time asymptotic convergence rate. Precisely, this convergence rate is completely same as the spatial convergence rate of the initial perturbation. The second result is that if the initial data is given by the Riemann data, an admissible weak solution, which has a discontinuity, converges to the travelling wave exponentially fast. Both of two results are proved by obtaining decay estimates in time through energy methods with suitably chosen weight functions. Copyright © 2006 John Wiley & Sons, Ltd.

In this paper, we study the growth behaviour of entire Clifford algebra-valued solutions to iterated Dirac and generalized Cauchy–Riemann equations in higher-dimensional Euclidean space. Solutions to this type of systems of partial differential equations are often called k-monogenic functions or, more generically, polymonogenic functions. In the case dealing with the Dirac operator, the function classes of polyharmonic functions are included as particular subcases. These are important for a number of concrete problems in physics and engineering, such as, for example, in the case of the biharmonic equation for elasticity problems of surfaces and for the description of the stream function in the Stokes flow regime with high viscosity. Furthermore, these equations in turn are closely related to the polywave equation, the poly-heat equation and the poly-Klein–Gordon equation. In the first part we develop sharp Cauchy-type estimates for polymonogenic functions, for equations in the sense of Dirac as well as Cauchy–Riemann. Then we introduce generalizations of growth orders, of the maximum term and of the central index in this framework, which in turn then enable us to perform a quantitative asymptotic growth analysis of this function class. As concrete applications we develop some generalizations of some of Valiron's inequalities in this paper. Copyright © 2006 John Wiley & Sons, Ltd.

The aim of this paper is to derive, in the Hilbert space setting, an integral representation formula for the effective elasticity tensor for a two-component composite of elastic materials, not necessarily well-ordered. This integral representation formula implies a relation which links the effective elastic moduli to the N-point correlation functions of the microstructure. Such relation not only facilitates a powerful scheme for systematic incorporation of microstructural information into bounds on the effective elastic moduli but also provides a theoretical foundation for inverse-homogenization. The analysis presented in this paper can be generalized to an n-component composite of elastic materials. The relations developed here can be applied to the inverse-homogenization for a special class of linear viscoelastic composites. The results will be presented in another paper. Copyright © 2005 John Wiley & Sons, Ltd.

SUMMARY 9 In this paper we investigate the unknown body problem in a wave guide where one boundary has a pressure release condition and the other an impedance condition. The method used in the paper for 11 solving the unknown body inverse problem is the intersection canonical body approximation (ICBA). The ICBA is based on the Rayleigh conjecture, which states that every point on an illuminated body 13 radiates sound from that point as if the point lies on its tangent sphere. The ICBA method requires that an analytical solution be known exterior to a canonical body in the wave guide. We use the sphere of 15 arbitrary centre and radius in the wave guide as our canonical body. We are lead then to analytically computing the exterior solution for a sphere between two parallel plates. We use the ICBA to construct 17 solutions at points ranging over the suspected surface of the unknown object to reconstruct the unknown

In this paper we prove an existence result of positive periodic solutions to second order differential equations with certain strong repulsive singularities near the origin and with some semilinear growth near infinity. Different from the nonsingular case, the result in this paper shows that both of the periodic and the antiperiodic eigenvalues play the same role in such an existence result. Copyright © 2003 John Wiley & Sons, Ltd.

This paper is the third in a series of several works devoted to the asymptotic and spectral analysis of a model of an aircraft wing in a subsonic air flow. This model has been developed in the Flight Systems Research Center of UCLA and is presented in the works by Balakrishnan. The model is governed by a system of two coupled integro-differential equations and a two-parameter family of boundary conditions modeling the action of the self-straining actuators. The differential parts of the above equations form a coupled linear hyperbolic system; the integral parts are of the convolution type. The system of equations of motion is equivalent to a single operator evolution-convolution equation in the energy space. The Laplace transform of the solution of this equation can be represented in terms of the so-called generalized resolvent operator, which is an operator-valued function of the spectral parameter. This generalized resolvent operator is a finite-meromorphic function on the complex plane having the branch cut along the negative real semi-axis. Its poles are precisely the aeroelastic modes and the residues at these poles are the projectors on the generalized eigenspaces. In the first two papers (see [33, 34]) and in the present one, our main object of interest is the dynamics generator of the differential parts of the system. This generator is a non-self-adjoint operator in the energy space with a purely discrete spectrum. In the first paper, we have shown that the spectrum consists of two branches, and have derived their precise spectral asymptotics with respect to the eigenvalue number. In the second paper, we have derived the asymptotical approximations for the mode shapes. Based on the asymptotical results of the first two papers, in the present paper, we (a) prove that the set of the generalized eigenvectors of the aforementioned differential operator is complete in the energy space; (b) construct the set of vectors which is biorthogonal to the set of the generalized eigenvectors in the case when theremight be not only eigenvectors but associate vectors as well; and (c) prove that the set of the generalized eigenvectors forms a Riesz basis in the energy space. To prove the main result of the paper, we made use of the Nagy-Foias functional model for non-self-adjoint operators. The results of all three papers will be important for the reconstruction of the solution of the original initial-boundary-value problem from its Laplace transform in the forthcoming papers.

In this paper we show that every variational solution of the steady-state Boussinesq equations (u, p, θ) with thermocapillarity effect on the surface of the liquid has the following regularity: u ∈ H2(Ω)2, p ∈ H1(Ω), θ ∈ H2(Ω) under appropriate hypotheses on the angles of the ‘2-D’ container (a cross-section of the 3-D container in fact) and of the horizontal surface of the liquid with the inner surface of the container. The difficulty comes from the boundary condition on the surface of the liquid (e.g. water) which modelizes the thermocapillarity effect on the surface of the liquid (equation (68.10) of Levich [7]). More precisely we will show that u ∈ P22(Ω)2 and that θ ∈ P22(Ω), where P22(Ω) denotes the usual Kondratiev space. This result will be used in a forthcoming paper to prove convergence results for finite element methods intended to compute approximations of a non-singular solution [1] of this problem. Copyright © 1999 John Wiley & Sons, Ltd.

The paper consists of two parts. In the first part we investigate a Nystrom- or product integration method for second kind singular integral equations. We prove an asymptotically optimal error estimate in the scale of Sobolev Hilbert spaces. Although the result can also be obtained as a special case of a discrete iterated collocation method our proof is more direct and uses the Nystrom interpolation. In the second part of this paper we consider the Dirichlet problem for thin elastic plates with transverse shear deformation. The boundary value problem is transformed into a 3 x 3 system of singular Fredholm integral equations of second kind. After discussing existence and uniqueness of the solution to the integral equations in a Sobolev space setting, we apply the Nystrom method to solve the integral equations numerically.

Consider the two adjacent rectangular wedges K1, K2 with common edge in the upper halfspace of ℝ3 and the operator A (=−Laplacian multiplied by different constant coefficients a1, a2 in K1, K2, respectively) acting on a subspace of ∏2j=1L2(Kj). This subspace should consist of those sufficiently regular functions u=(u1,u2) satisfying the homogeneous Dirichlet boundary condition on the bottom of the upper halfspace. Moreover, the coincidence of u1 and u2 along the interface of the two wedges is prescribed as well as a transmission condition relating their first one-sided derivatives. We interpret the corresponding wave equation with A defining its spatial part as a simple model for wave propagation in two adjacent media with different material constants. In this paper it is shown (by Friedrichs' extension) that A is selfadjoint in a suitable Hilbert space. Applying the Fourier (-sine) transformations we reduce our problem with singularities along the z-axis to a non-singular Klein–Gordon equation in one space dimension with potential step. The resolvent, the limiting absorption principle and expansion in generalized eigenfunctions of A are derived (by Plancherel theory) from the corresponding results concerning the latter equation in one space dimension. An application of the spectral theorem for unbounded selfadjoint operators on Hilbert spaces yields the solution of the time dependent problem with prescribed initial data. The paper is concluded by a discussion of the relation between the physical geometry of the problem and its spectral properties. © 1997 by B. G. Teubner Stuttgart–John Wiley & Sons Ltd.

This paper concerns the well-posedness of the hydrodynamic model for semiconductor devices, a quasilinear elliptic-parbolic-hyperbolic system. Boundary conditions for elliptic and parabolic equations are Dirichlet conditions while boundary conditions for the hyperbolic equations are assumed to be well-posed in L2 sense. Maximally strictly dissipative boundary conditions for the hyperbolic equations satisfy the assumption of well-posedness in L2 sense. The well-posedness of the model under the boundary conditions is demonstrated. This paper addresses the well-posedness of the hydrodynamic model for semiconductors. The model is derived from moments of the Boltzmann’s equation, taken over group velocity space. When coupled with the charge conservation equation, it describes the behaviour of small semiconductor devices and accounts for special features such as hot electrons and velocity overshoots. The model consists of a set of non-linear conservation laws for particle number, momentum, and energy, coupled to Poisson’s equation for the electric potential. It is a perturbation of the drift diffusion model [7]. We consider a ballistic diode problem which models the channel of a MOSFET, so the effect of holes in the model can be neglected. The model is [4,11]

This paper is concerned with the solution of a boundary transmission problem in an infinite wedge. We treat this problem by a boundary integral method using Green's contact function for two half-spaces. The integral operators are studied via a harmonic analysis approach which goes back to a paper of Fabes et al. We improve their results studying the Fourier symbol of the associated integral operators on the half-plane. This leads to invertibility criteria for the boundary integral operators.

In this paper, we establish existence and finite time blow up of weak solutions of a parabolic equation of p(x)-Laplacian type with the Dirichlet boundary condition. Moreover, we obtain upper and lower bounds for the blow up time of solutions, by employing concavity method and differential inequality technique respectively.

The interest in the use of quasimodes, or almost frequencies and almost eigenfunctions, to describe asymptotics for low-frequency and high-frequency vibrations in certain singularly perturbed spectral problems, which depend on a small parameter e, has been recently highlighted in many papers. In this paper we deal with the low frequencies for a Steklov-type eigenvalue homogenization problem: we consider harmonic functions in a bounded domain of ℝ2, and strongly alternating boundary conditions of the Dirichlet and Steklov type on a part of the boundary. The spectral parameter appears in the boundary condition on small segments Te of size O(e) periodically distributed along the boundary; e also measures the periodicity of the structure. We consider associated second-order evolution problems on spaces of traces that depend on e, and we provide estimates for the time t in which standing waves, constructed from quasimodes, approach their solutions ue(t) as e0. Copyright © 2009 John Wiley & Sons, Ltd.

In this paper we give a proof of the global existence of weak solutions for the semiconductor Boltzmann equation. This equation rules the evolution of the distribution function of carriers in the kinetic model of semiconductors. The main tool for the proof consists of a recent compactness result on velocity averages of solutions of transport equations. This result needs a L2-estimate of the electric field, which is obtained from the energy estimate, using the original regularization procedure of the problem, proposed in this paper.

In the paper, we consider the local-in-time and the global-in-time infinity-ion-mass convergence of bipolar Euler-Maxwell systems by setting the mass of an electron me=1 and letting the mass of an ion mi→∞. We use the method of asymptotic expansions to handle the local-in-time convergence problem and find that the limiting process from bipolar models to unipolar models is actually decoupling, but not the vanishing of equations for the corresponding the other particle. Moreover, when the initial data is sufficiently close to the constant equilibrium state, we establish the global-in-time infinity-ion-mass convergence.

In this paper, we study the following Schrodinger-Kirchhoff–type equation with critical or supercritical growth −(a+b∫R3|∇u|2dx)△u+V(x)u=f(x,u)+λ|u|p−2u,x∈R3, where a>0, b>0, λ>0, and p≥6. Under some suitable conditions, we prove that the equation has a nontrivial solution for small λ>0 by variational method. Moreover, we regard b as a parameter and obtain a convergence property of the nontrivial solution as b↘0. Our main contribution is related to the fact that we are able to deal with the case p>6.

An efficient method for nonlinear fractional differential equations is proposed in this paper. This method consists of 2 steps. First, we linearize the nonlinear operator equation by quasi-Newton's method, which is based on Frechet derivative. Then we solve the linear fractional differential equations by the simplified reproducing kernel method. The convergence of the quasi-Newton's method is discussed for the general nonlinear case as well. Finally, some numerical examples are presented to illustrate accuracy, efficiency, and simplicity of the method.

In this paper, we study the following fractional Schrodinger equations: (−△)αu+λV(x)u=κ|u|q−2u|x|s+β|u|2α∗−2u,u∈Hα(RN),N⩾3,(1) where (−△)α is the fractional Laplacian operator with α∈(0,1),2≤q≤2α,s∗=2(N−s)N−2α≤2α∗=2NN−2α, 0≤s≤2α, λ>0, κ and β are real parameter. 2α∗ is the critical Sobolev exponent. We prove a fractional Sobolev-Hardy inequality and use it together with concentration compact theory to get a ground state solution. Moreover, concentration behaviors of nontrivial solutions are obtained when the coefficient of the potential function tends to infinity.

In this paper, we investigate the existence and multiplicity of harmonic and subharmonic solutions for second-order quasilinear equation (ϕp(x′))′+g(x)=e(t), where ϕp:R→R,ϕp(u)=|u|p−2u,p>1, g satisfies the superlinear condition at infinity. We prove that the given equation possesses harmonic and subharmonic solutions by using the phase-plane analysis methods and a generalized version of the Poincare-Birkhoff twist theorem.

In this paper, we study the existence of a positive ground state solution to the following coupled system of nonlinear Schrodinger equations: −Δu+V1(x)u=f1(x,u)+λ(x)v,x∈R2,−Δv+V2(x)v=f2(x,v)+λ(x)u,x∈R2, where the nonlinearities f1(x,s) and f2(x,s) are superlinear at infinity and have exponential critical growth of the Trudinger-Moser type. The potentials V1(x) and V2(x) are nonnegative and satisfy a condition involving the coupling term λ(x), namely, λ(x)2

This paper presents 2 new classes of the Bessel functions on a compact domain [0,T] as generalized-tempered Bessel functions of the first- and second-kind which are denoted by GTBFs-1 and GTBFs-2. Two special cases corresponding to the GTBFs-1 and GTBFs-2 are considered. We first prove that these functions are as the solutions of 2 linear differential operators and then show that these operators are self-adjoint on suitable domains. Some interesting properties of these sets of functions such as orthogonality, completeness, fractional derivatives and integrals, recursive relations, asymptotic formulas, and so on are proved in detail. Finally, these functions are performed to approximate some functions and also to solve 3 practical differential equations of fractionalorders.

In this paper, we derive an asymptotic expansion for the semi-infinite sum of Dirac-δ functions centered at discrete equidistant points defined by the set Na={x∈R:∃n∈N∧x=na,∀a>0}. The method relies on the Laplace transform of the semi-infinite sum of Dirac-δ functions. The derived series distribution takes the form of the Euler-Maclaurin summation when the distributions are defined for complex or real-valued continuous functions over the interval [0,∞). For n=1, the series expansion contributes with a term equal to δ(x)/2, which survives in the limit when a→0+. This term represents a correction term, which is in general omitted in calculations of the density of states of quantum confined systems by finite-size effects.

This paper is concerned with the following nonlinear fractional Schrodinger equation e2s(−Δ)su+V(x)u=|u|p−2u,inRN, where e>0 is a small parameter, V(x) is a positive function, 0 2s). Under some suitable conditions, we prove that for any positive integer k, one can construct a nonradial sign-changing (nodal) solutions with exactly k maximum points and k minimum points near the local minimum point of V(x).

In this paper, we consider the integration of systems of second-order linear inhomogeneous initial value problems with constant coefficients. Hybrid Numerov methods are used that are constructed in the sense of Runge-Kutta ones. Thus, the Taylor expansions at the internal points are matched properly in the final expression. We present the order conditions taking advantage of the special structure of the problem at hand. These equations are solved using differential evolution technique, and we present a method with algebraic order eighth at a cost of only 5 function evaluations per step. Numerical results over some linear problems, especially arising from the semidiscretization of the wave equation indicate the superiority of the new method.

This paper presents a method for computing numerical solutions of two-dimensional Stratonovich Volterra integral equations using one-dimensional modification of hat functions and two-dimensional modification of hat functions. The problem is transformed to a linear system of algebraic equations using the operational matrix associated with one-dimensional modification of hat functions and two-dimensional modification of hat functions. The error analysis of the method is given. The method is computationally attractive, and applications are demonstrated by a numerical example. Copyright © 2017 John Wiley & Sons, Ltd.

In this paper, we study the dynamics of a Nicholson's blowflies equation with state-dependent delay. For the constant delay, it is known that a sequence of Hopf bifurcation occurs at the positive equilibrium as the delay increases and global existence of periodic solutions has been established. Here, we consider the state-dependent delay instead of the constant delay and generalize the results on the existence of slowly oscillating periodic solutions under a set of mild conditions on the parameters and the delay function. In particular, when the positive equilibrium gets unstable, a global unstable manifold connects the positive equilibrium to a slowly oscillating periodic orbit. Copyright © 2017 John Wiley & Sons, Ltd.

In this paper we consider the inviscid limit for the periodic solutions to Navier-Stokes equation in the framework of Gevrey class. It is shown that the lifespan for the solutions to Navier-Stokes equation is independent of viscosity, and that the solutions of the Navier-Stokes equation converge to that of Euler equation in Gevrey class as the viscosity tends to zero. Moreover the convergence rate in Gevrey class is presented.

In this paper, a second-order fast explicit operator splitting method is proposed to solve the mass-conserving Allen–Cahn equation with a space–time-dependent Lagrange multiplier. The space–time-dependent Lagrange multiplier can preserve the volume of the system and keep small features. Moreover, we analyze the discrete maximum principle and the convergence rate of the fast explicit operator splitting method. The proposed numerical scheme is of spectral accuracy in space and of second-order accuracy in time, which greatly improves the computational efficiency. Numerical experiments are presented to confirm the accuracy, efficiency, mass conservation, and stability of the proposed method. Copyright © 2017 John Wiley & Sons, Ltd.

In this paper, we prove the existence and uniqueness for the global solutions of Cauchy problem for coupled nonlinear Schrodinger equations and obtain the continuous dependence result on the initial data and the stronger decay estimate of global solutions. In particular, we show the existence and uniqueness of self-similar solutions. Also, we build some asymptotically self-similar solutions. Copyright © 2017 John Wiley & Sons, Ltd.

In this paper, we consider the compressible bipolar Navier–Stokes–Poisson equations with a non-flat doping profile in three-dimensional space. The existence and uniqueness of the non-constant stationary solutions are established when the doping profile is a small perturbation of a positive constant state. Then under the smallness assumption of the initial perturbation, we show the global existence of smooth solutions to the Cauchy problem near the stationary state. Finally, the convergence rates are obtained by combining the energy estimates for the nonlinear system and the L2-decay estimates for the linearized equations. Copyright © 2017 John Wiley & Sons, Ltd.

The main purpose of this paper is to analyze the convergence and regularity of our proposed algorithm of the finite element methods coupled with a theta time discretization scheme for evolutionary Hamilton-Jacobi-Bellman equations with linear source terms with respect to the Dirichlet boundary conditions (Appl. Math. Comput., 262 (2015), 42.55 ). Also, an optimal error estimate with an asymptotic behavior in uniform norm is given. Copyright © 2017 John Wiley & Sons, Ltd.

The aim of this paper is twofold. We first establish the Besov spaces on metric spaces endowed with a doubling measure, via the remarkable orthonormal wavelet basis constructed recently by T. Hytonen and O. Tapiola, and characterize the dual spaces of these Besov spaces. Second, we prove the T1 type theorem for the boundedness of Calderon–Zygmund operators on these Besov spaces. Finally, we introduce a new class of Lipschitz spaces and characterize these spaces via the Littlewood–Paley theory. Copyright © 2016 John Wiley & Sons, Ltd.

This paper presents a computational technique for the solution of the nonlinear mixed Volterra–Fredholm integral equations of the second kind. Using the properties of three-dimensional modification of hat functions, these are types of equations to a nonlinear system of algebraic equations. Also, convergence results and error analysis are discussed. The efficiency and accuracy of the proposed method is illustrated by numerical examples. Copyright © 2016 John Wiley & Sons, Ltd.

In this paper, new Lyapunov-type inequalities are obtained for the case when one is dealing with a class of fractional two-point boundary value problems. As an application of this result, we obtain a lower bound for the eigenvalues of corresponding equations. Copyright © 2016 John Wiley & Sons, Ltd.

This paper is devoted to the analysis of complex dynamics of a generalized Lorenz–Stenflo hyperchaotic system. First, on the local dynamics, the bifurcation of periodic solutions at the zero-zero-Hopf equilibrium (that is, an isolated equilibrium with double zero eigenvalues and a pair of purely imaginary eigenvalues) of this hyperchaotic system is investigated, and the sufficient conditions, which insure that two periodic solutions will bifurcate from the bifurcation point, are obtained. Furthermore, on the global dynamics, the explicit ultimate bound sets of this hyperchaotic system are obtained. Copyright © 2016 John Wiley & Sons, Ltd.

We present a new Lyapunov function for laminar flow, in the x-direction, between two parallel planes in the presence of a coplanar magnetic field for three-dimensional perturbations with stress-free boundary planes that provides conditional nonlinear stability for all Reynolds numbers(Re) and magnetic Reynolds numbers(Rm) below π2/2M. Compared with previous results on the nonlinear stability of this problem, the radius of stability ball and the energy decay rate obtained in this paper are independent of the magnetic field. Copyright © 2016 John Wiley & Sons, Ltd.