Authors:Jen-Yuan Chen; David R. Kincaid; Bei-Ru Lin Pages: 1 - 5 Abstract: Publication date: May 2018 Source:Applied Mathematics Letters, Volume 79 Author(s): Jen-Yuan Chen, David R. Kincaid, Bei-Ru Lin We propose a new variant of Newton’s method based on Simpson’s three-eighth rule. It can be shown that the new method is cubically convergent.

Authors:Zhongzhou Lan; Bo Gao Pages: 6 - 12 Abstract: Publication date: May 2018 Source:Applied Mathematics Letters, Volume 79 Author(s): Zhongzhou Lan, Bo Gao Under investigation in this paper is a ( 2 + 1 ) -dimensional Heisenberg ferromagnetic spin chain equation with time-dependent coefficients. Based on the symbolic computation, Lax pair and infinitely many conservation laws are constructed. Multi-soliton solutions are derived by virtue of the Darboux transformation. Propagation and interaction properties of the solitons are discussed. Amplitude of the soliton is determined by the spectral parameter and wave number, while the velocity is related to both these parameters and the time-dependent coefficients. Elastic interactions between the two solitons are displayed, and their amplitudes keep unchanged after the interaction except for the phase shifts.

Authors:Meng Liu; Yu Zhu Pages: 13 - 19 Abstract: Publication date: May 2018 Source:Applied Mathematics Letters, Volume 79 Author(s): Meng Liu, Yu Zhu A budworm growth model perturbed by both white noises and regime switchings is proposed and analyzed. It is proven that there is a threshold. If this threshold is positive, then the model has a unique ergodic stationary distribution; if this threshold is negative, then the zero solution of the model is stable. The results show that both white noises and regime switchings can change the stability of the model greatly. Several numerical simulations based on realistic data are also introduced to illustrate the main results.

Authors:Wenjie Hu; Yinggao Zhou Pages: 20 - 26 Abstract: Publication date: May 2018 Source:Applied Mathematics Letters, Volume 79 Author(s): Wenjie Hu, Yinggao Zhou The present work is devoted to the stability and attractivity analysis of a nonlocal delayed reaction–diffusion equation (DRDE) with a non-monotone bistable nonlinearity that describes the population dynamics for a two-stage species with Allee effect. By the idea of relating the dynamics of the nonlinear term to the DRDE and some stability results for the monostable case, we describe some basin of attractions for the DRDE. Additionally, existence of heteroclinic orbits and periodic oscillations are also obtained. Numerical simulations are also given at last to verify our theoretical results.

Authors:Jianhua Chen; Xianhua Tang; Bitao Cheng Pages: 27 - 33 Abstract: Publication date: May 2018 Source:Applied Mathematics Letters, Volume 79 Author(s): Jianhua Chen, Xianhua Tang, Bitao Cheng In this paper, we study the following quasilinear Schrödinger equation − Δ u + u − Δ ( u 2 ) u = h ( u ) , x ∈ R N , where N ≥ 3 , 2 ∗ = 2 N N − 2 , h is a continuous function. By using a change of variable, we obtain the existence of ground state solutions. Unlike the condition lim u → ∞ ∫ 0 u h ( s ) d s u 4 = ∞ , we only need to assume that lim u → ∞ ∫ 0 u h ( s ) d s u 2 = ∞ .

Authors:Longjie Xie Pages: 34 - 42 Abstract: Publication date: May 2018 Source:Applied Mathematics Letters, Volume 79 Author(s): Longjie Xie By using the Krylov estimate, we prove the exponential ergodicity of the invariant measure for stochastic Langevin equation with singular coefficients, where the classical Lyapunov condition cannot be verified.

Authors:Zhiyong Wang; Jihui Zhang Pages: 43 - 50 Abstract: Publication date: May 2018 Source:Applied Mathematics Letters, Volume 79 Author(s): Zhiyong Wang, Jihui Zhang In this paper, we are concerned with the existence of periodic solutions for the following non-autonomous second order Hamiltonian systems u ̈ ( t ) + ∇ F ( t , u ( t ) ) = 0 , a.e. t ∈ [ 0 , T ] , u ( 0 ) − u ( T ) = u ̇ ( 0 ) − u ̇ ( T ) = 0 , where F : R × R N → R is T -periodic ( T > 0 ) in its first variable for all x ∈ R N . When potential function F ( t , x ) is either locally in t asymptotically quadratic or locally in t superquadratic, we show that the above mentioned problem possesses at least one T -periodic solutions via the minimax methods in critical point theory, specially, a new saddle point theorem which is introduced in Schechter (1998).

Authors:Djillali Bouagada; Samuel Melchior; Paul Van Dooren Pages: 51 - 57 Abstract: Publication date: May 2018 Source:Applied Mathematics Letters, Volume 79 Author(s): Djillali Bouagada, Samuel Melchior, Paul Van Dooren We present an efficient algorithm to compute the H ∞ norm of a fractional system. The algorithm is based on the computation of level sets of the maximum singular value of the transfer function, as a function of frequency. Numerical examples are given to illustrate the new method.

Authors:Liguang Xu; Wen Liu Pages: 58 - 66 Abstract: Publication date: May 2018 Source:Applied Mathematics Letters, Volume 79 Author(s): Liguang Xu, Wen Liu This paper concerns with the ultimate boundedness problem for impulsive fractional delay differential equations. Based on the impulsive fractional differential inequality, the boundedness of Mittag-Leffler functions, and the successful construction of suitable Lyapunov functionals, some algebraic criteria are derived for testing the global ultimate boundedness of the equations, and the estimations of the global attractive sets are provided as well. One example is also given to show the effectiveness of the obtained theoretical results.

Authors:Shi Sun; Ziping Huang; Cheng Wang Pages: 67 - 72 Abstract: Publication date: May 2018 Source:Applied Mathematics Letters, Volume 79 Author(s): Shi Sun, Ziping Huang, Cheng Wang The purpose of this paper is to study the weak Galerkin finite element method for a class of quasilinear elliptic problems. The weak Galerkin finite element scheme is proved to have a unique solution with the assumption that guarantees the corresponding operator to be strongly monotone and Lipschitz-continuous. An optimal error estimate in a mesh-dependent energy norm is established. Some numerical results are presented to confirm the theoretical analysis.

Authors:Guanggang Liu; Yong Li; Xue Yang Pages: 73 - 79 Abstract: Publication date: May 2018 Source:Applied Mathematics Letters, Volume 79 Author(s): Guanggang Liu, Yong Li, Xue Yang In this paper we consider a class of super-linear second order Hamiltonian systems. We use Morse theory to obtain the existence and multiplicity of rotating periodic solutions, which might be periodic, subharmonic or quasi-periodic ones.

Authors:A.M. Khludnev; V.V. Shcherbakov Pages: 80 - 84 Abstract: Publication date: May 2018 Source:Applied Mathematics Letters, Volume 79 Author(s): A.M. Khludnev, V.V. Shcherbakov The note is concerned with a model of linear elastostatics for a two-dimensional inhomogeneous anisotropic body weakened by a single straight crack. On the crack faces, nonpenetration conditions/Signorini conditions are imposed. Relying upon a higher regularity result in Besov spaces for the displacement field in a neighborhood of the crack tip, we prove that the energy release rate is actually independent of the choice of a subsequent crack path (among the possible continuations of class H 3 ).

Authors:Moon-Jin Kang Pages: 85 - 91 Abstract: Publication date: May 2018 Source:Applied Mathematics Letters, Volume 79 Author(s): Moon-Jin Kang This article provides a rigorous justification on a hydrodynamic limit from the Vlasov–Poisson system with strong local alignment to the pressureless Euler–Poisson system for repulsive dynamics.

Authors:Lin Liu; Fawang Liu Pages: 92 - 99 Abstract: Publication date: May 2018 Source:Applied Mathematics Letters, Volume 79 Author(s): Lin Liu, Fawang Liu A novel investigation about the boundary layer flow of fractional Maxwell fluid over a stretching sheet with variable thickness is presented. By introducing new variables, the irregular boundary changes as a regular one. Solutions of the governing equations are obtained numerically where the L1-scheme is applied. Dynamic characteristicswith the effects of different parameters are shown by graphical illustrations. Three kinds of distributions versus power law parameter are presented, including monotonically increasing in nearly linear form at y =1, increasing at first and then decreasing at y =1.4 and monotonically decreasing in nearly linear form at y =2.

Authors:Deyue Zhang; Fenglin Sun; Linyan Lu; Yukun Guo Pages: 100 - 104 Abstract: Publication date: May 2018 Source:Applied Mathematics Letters, Volume 79 Author(s): Deyue Zhang, Fenglin Sun, Linyan Lu, Yukun Guo This paper concerns a boundary value problem of Laplace’s equation, which is solved by determining the unknown coefficients in the expansion of harmonic polynomials. A regularization method is proposed to tackle the resulting ill-posed linear system. The stability and convergence results are provided and a validating numerical experiment is presented.

Authors:Shuai Yang; Liping Wang; Shuqin Zhang Pages: 105 - 110 Abstract: Publication date: May 2018 Source:Applied Mathematics Letters, Volume 79 Author(s): Shuai Yang, Liping Wang, Shuqin Zhang The conformable derivative is used to develop the Swartzendruber model for description of non-Darcian flow in porous media. The proposed conformable Swartzendruber models are solved employing the Laplace transform method and validated on the basis of water flow in compacted fine-grained soils. The results of fitting analysis present a good agreement with experimental data. Furthermore, sensitivity analyses are carried out to illustrate the effects of related parameters on the conformable Swartzendruber models.

Authors:J. Deteix; D. Yakoubi Pages: 111 - 117 Abstract: Publication date: May 2018 Source:Applied Mathematics Letters, Volume 79 Author(s): J. Deteix, D. Yakoubi The incremental projection scheme and its enhanced version, the rotational projection scheme are powerful and commonly used approaches producing efficient numerical algorithms for solving the Navier–Stokes equations. However, the much improved rotational projection scheme cannot be used on models with non-homogeneous viscosity, imposing the use of the less accurate incremental projection. This paper presents a projection method for the Navier–Stokes equations for fluids having variable viscosity, giving a consistent pressure and increased accuracy in pressure when compared to the incremental projection. The accuracy of the method will be illustrated using a manufactured solution.

Authors:Zhenya Yan Pages: 123 - 130 Abstract: Publication date: May 2018 Source:Applied Mathematics Letters, Volume 79 Author(s): Zhenya Yan We use two families of parameters { ( ϵ x j , ϵ t j ) ϵ x j , t j = ± 1 , j = 1 , 2 , … , n } to first introduce a unified novel hierarchy of two-family-parameter equations (simply called Q ϵ x n → , ϵ t n → ( n ) hierarchy), connecting integrable local, nonlocal, novel mixed-local–nonlocal, and other nonlocal vector nonlinear Schrödinger (VNLS) equations. The Q ϵ x n → , ϵ t n → ( n ) system with ( ϵ x j , ϵ t j ) = ( ± 1 , 1 ) , j = 1 , 2 , … , n is shown to possess Lax pairs and infinite number of conservation laws. Moreover, we also analyze the P T symmetry of the Hamiltonians with self-induced potentials. The multi-linear forms and some symmetry reductions are also studied. In fact, the used two families of parameters can also be extended to the general case { ( ϵ x j , ϵ t j ) ϵ x j = e i θ x j , ϵ t j = e i θ t j , θ x j , θ t j ∈ [ 0 , 2 π ) , j = 1 , 2 , … , n } to generate more types of nonlinear equations. The novel two-family-parameter (or multi-family-parameter for higher-dimensional cases) idea can also be applied to other local nonlinear evolution equations to find novel integrable and non-integrable nonlocal and mixed-local–nonlocal systems.

Authors:Xi-An Li; Wei-Hong Zhang; Yu-Jiang Wu Pages: 131 - 137 Abstract: Publication date: May 2018 Source:Applied Mathematics Letters, Volume 79 Author(s): Xi-An Li, Wei-Hong Zhang, Yu-Jiang Wu For solving a class of complex symmetric linear system, we first transform the system into a block two-by-two real formulation and construct a symmetric block triangular splitting (SBTS) iteration method based on two splittings. Then, eigenvalues of iterative matrix are calculated, convergence conditions with relaxation parameter are derived, and two optimal parameters are obtained. Besides, we present the optimal convergence factor and test two numerical examples to confirm theoretical results and to verify the high performances of SBTS iteration method compared with two classical methods.

Authors:Xiu Yang; Haitao Qi; Xiaoyun Jiang Pages: 1 - 8 Abstract: Publication date: April 2018 Source:Applied Mathematics Letters, Volume 78 Author(s): Xiu Yang, Haitao Qi, Xiaoyun Jiang The electroosmotic flow of fractional Maxwell fluid in a rectangular microchannel is studied in this paper. By means of the fractional Maxwell constitutive equation, and based on the experimental data, the nonlinear conjugate gradient method is proposed to get the viscoelastic parameters. Combined with the continuity equations and Cauchy momentum equations, the governing equations of velocity distribution are established. Besides, a fully discrete spectral method based on a difference method in the temporal direction and a Legendre spectral method in the spatial direction is introduced to solve the dimensionless governing equations. Finally, some results are presented to show the effectiveness of the proposed method.

Authors:Xinchen Zhou; Zhaoliang Meng; Xin Fan; Zhongxuan Luo Pages: 9 - 15 Abstract: Publication date: April 2018 Source:Applied Mathematics Letters, Volume 78 Author(s): Xinchen Zhou, Zhaoliang Meng, Xin Fan, Zhongxuan Luo A simple nonconforming brick element is proposed for 3D Stokes equations. This element has 15 degrees of freedom and reaches the lowest approximation order. In the mixed scheme for Stokes equations, we adopt our new element to approximate the velocity, along with the discontinuous piecewise constant element for the pressure. The stability of this scheme is proved and thus the optimal convergence rate is achieved. A numerical example verifies our theoretical analysis.

Authors:Pin Lyu; Seakweng Vong Pages: 16 - 23 Abstract: Publication date: April 2018 Source:Applied Mathematics Letters, Volume 78 Author(s): Pin Lyu, Seakweng Vong In this paper, we consider the generalized Benjamin–Bona–Mahony (BBM) equation with a fractional order derivative in time. By introducing a weighted approach and basing on the L 2 - 1 σ formula, a linearized finite difference scheme is proposed to solve the nonlinear problem. The scheme is shown to be unconditionally convergent with second-order in time and space within maximum-norm estimate.

Authors:Dongho Kim; Eun-Jae Park; Boyoon Seo Pages: 24 - 30 Abstract: Publication date: April 2018 Source:Applied Mathematics Letters, Volume 78 Author(s): Dongho Kim, Eun-Jae Park, Boyoon Seo In this paper, we prove optimal a priori error estimates for the pseudostress-velocity mixed finite element formulation of the incompressible Navier–Stokes equations, thus improve the result of Cai et al. (SINUM 2010). This is achieved by applying Petrov–Galerkin type Brezzi–Rappaz–Raviart theory.

Authors:Jishan Fan; Fucai Li Pages: 31 - 35 Abstract: Publication date: April 2018 Source:Applied Mathematics Letters, Volume 78 Author(s): Jishan Fan, Fucai Li In this short paper we establish the global well-posedness of strong solutions to the 3D full compressible Navier–Stokes system with vacuum in a bounded domain Ω ⊂ R 3 by the bootstrap argument provided that the viscosity coefficients λ and μ satisfy that 7 λ > 9 μ and the initial data ρ 0 and u 0 satisfy that ‖ ρ 0 ‖ L ∞ ( Ω ) and ‖ ρ 0 u 0 5 ‖ L 1 ( Ω ) are sufficiently small.

Authors:Yan-Fang Li; Zhong-Jie Han; Gen-Qi Xu Pages: 51 - 58 Abstract: Publication date: April 2018 Source:Applied Mathematics Letters, Volume 78 Author(s): Yan-Fang Li, Zhong-Jie Han, Gen-Qi Xu The large-time behavior of a 1-d coupled string-beam system is considered. Combining a detailed spectral analysis with resolvent estimation, we obtain two kinds of energy decay rates of the string-beam system with different locations of the frictional damping. On one hand, if the frictional damping is only actuated in the beam part, the system lacks exponential decay. Specifically, the optimal polynomial decay rate t − 1 is obtained under smooth initial conditions. On the other hand, if the frictional damping is only effective in the string part, the exponential decay of energy is presented. Some numerical simulations are given to support these results.

Authors:Congchong Guo; Ming Lu; Xiangxiang Guo Pages: 59 - 64 Abstract: Publication date: April 2018 Source:Applied Mathematics Letters, Volume 78 Author(s): Congchong Guo, Ming Lu, Xiangxiang Guo In this paper, we establish the global regularity of classical solutions for the two-dimensional MHD equations with only velocity diffusion for a class of large initial data. Both the initial velocity and magnetic field can be arbitrarily large in H s .

Authors:S.A. Buterin Pages: 65 - 71 Abstract: Publication date: April 2018 Source:Applied Mathematics Letters, Volume 78 Author(s): S.A. Buterin A convolution integro-differential operator of the first order with a finite number of discontinuities is considered. Properties of its spectrum are studied and a uniqueness theorem is proven for the inverse problem of recovering the convolution kernel along with the boundary condition from the spectrum.

Authors:Dongxu Jia; Zhiqiang Sheng; Guangwei Yuan Pages: 72 - 78 Abstract: Publication date: April 2018 Source:Applied Mathematics Letters, Volume 78 Author(s): Dongxu Jia, Zhiqiang Sheng, Guangwei Yuan In this paper, a conservative parallel difference scheme, which is based on domain decomposition method, for 2-dimension diffusion equation is proposed. In the construction of this scheme, we use the numerical solution on the previous time step to give a weighted approximation of the numerical flux. Then the sub-problems with Neumann boundary are computed by fully implicit scheme. What is more, only local message communication is needed in the program. We use the method of discrete functional analysis to give the proof of the unconditional stability and second-order convergence accuracy. Some numerical tests are given to verify the theory results.

Authors:Qun Liu; Daqing Jiang Pages: 79 - 87 Abstract: Publication date: April 2018 Source:Applied Mathematics Letters, Volume 78 Author(s): Qun Liu, Daqing Jiang In this paper, we focus on a stochastic predator–prey model with distributed delay. We first obtain the existence of a stationary distribution to the positive solutions by stochastic Lyapunov function method. Then we establish sufficient conditions for extinction of the predator population, that is, the prey population is survival and the predator population is extinct.

Authors:Rui Li; Pengcheng Wang; Xinran Zheng; Bo Wang Pages: 88 - 94 Abstract: Publication date: April 2018 Source:Applied Mathematics Letters, Volume 78 Author(s): Rui Li, Pengcheng Wang, Xinran Zheng, Bo Wang It is of significance to explore benchmark analytic free vibration solutions of rectangular thick plates without two parallel simply supported edges, because the classic analytic methods are usually invalid for the problems of this category. The main challenge is to find the solutions meeting both the governing higher order partial differential equations (PDEs) and boundary conditions of the plates, i.e., to analytically solve associated complex boundary value problems of PDEs. In this letter, we extend a novel symplectic superposition method to the free vibration problems of clamped rectangular thick plates, with the analytic frequency solutions obtained by a brief set of equations. It is found that the analytic solutions of clamped plates can simply reduce to their variants with any combinations of clamped and simply supported edges via an easy relaxation of boundary conditions. The new results yielded in this letter are not only useful for rapid design of thick plate structures but also provide reliable benchmarks for checking the validity of other new solution methods.

Authors:C. Burgos; J. Calatayud; J.-C. Cortés; L. Villafuerte Pages: 95 - 104 Abstract: Publication date: April 2018 Source:Applied Mathematics Letters, Volume 78 Author(s): C. Burgos, J. Calatayud, J.-C. Cortés, L. Villafuerte The aim of this paper is to solve a class of non-autonomous linear fractional differential equations with random inputs. A mean square convergent series solution is constructed in the case that the fractional order α of that Caputo derivative lies in ] 0 , 1 ] using a random Fröbenius approach. The analysis is conducted by using the so-called mean square random calculus. The mean square convergence of the series solution is established assuming mild conditions on random inputs (diffusion coefficient and initial condition). We show that these conditions are satisfied for a variety of unbounded random variables. In addition, explicit expressions to approximate the mean, the variance and the covariance functions of the random series solution are given. Two full illustrative examples are shown.

Authors:Shaoli Wang; Fei Xu Pages: 105 - 111 Abstract: Publication date: April 2018 Source:Applied Mathematics Letters, Volume 78 Author(s): Shaoli Wang, Fei Xu In this paper, we investigate an impaired or immunosuppressive HIV infection model. By analyzing the model, we obtain two thresholds R 0 and R c . It is shown that R 0 determines whether the virus dies out. We also obtain the post-treatment control threshold and the elite control threshold. There exists a bistable interval between these two thresholds. When R 0 > R c , immune intensity is in the bistable interval, which implies that the system has bistable behavior and as such the virus is under post-treatment control. On the other hand, when the immune intensity is greater than the elite immune control threshold, virus will be under elite control. Our investigation shows that when antiviral therapy cannot completely clear the virus, introducing immunotherapy is an optimal choice.

Authors:Fu-Hong Lin; Shou-Ting Chen; Qi-Xing Qu; Jian-Ping Wang; Xian-Wei Zhou; Xing Lü Pages: 112 - 117 Abstract: Publication date: April 2018 Source:Applied Mathematics Letters, Volume 78 Author(s): Fu-Hong Lin, Shou-Ting Chen, Qi-Xing Qu, Jian-Ping Wang, Xian-Wei Zhou, Xing Lü Linear superposition principle is applied to the Hirota bilinear form of a new (3+1)-dimensional generalized Kadomtsev–Petviashvili equation, which leads to a sufficient and necessary criterion for the existence of linear subspaces of exponential traveling wave solutions. As a result, resonant multiple wave solutions are derived and plotted for the new (3+1)-dimensional generalized Kadomtsev–Petviashvili equation.

Authors:Jiang-Yan Song; Hui-Qin Hao; Xiao-Mei Zhang Pages: 126 - 132 Abstract: Publication date: April 2018 Source:Applied Mathematics Letters, Volume 78 Author(s): Jiang-Yan Song, Hui-Qin Hao, Xiao-Mei Zhang Under investigations in this paper is a discrete generalized nonlinear Schrödinger equation with variable coefficients. Through symbolic computation the discrete spectral problems are analyzed, the discrete N-fold Darboux transformation (DT) is constructed, discrete one and two-soliton solutions in the form of Vandermonde-like determinants are derived and some dynamic behaviors of those solitons are discussed graphically.

Authors:Lian-Li Feng; Tian-Tian Zhang Pages: 133 - 140 Abstract: Publication date: April 2018 Source:Applied Mathematics Letters, Volume 78 Author(s): Lian-Li Feng, Tian-Tian Zhang Under investigation in this paper is a coupled nonlinear Schrödinger (NLS) equation, which describes nonlinear pulse propagation in optical fibers by retaining terms up to the next leading asymptotic order. Based on the Lax pair of the coupled NLS equation, we construct the determinant representation of the N -fold Darboux transformation(DT). Furthermore, by using the obtained N -fold DT, we obtain its higher-order soliton, breather and rogue wave solutions. Finally, the dynamic characteristics of these solutions are discussed.

Authors:Chengyuan Qu; Wenshu Zhou; Bo Liang Pages: 141 - 146 Abstract: Publication date: April 2018 Source:Applied Mathematics Letters, Volume 78 Author(s): Chengyuan Qu, Wenshu Zhou, Bo Liang The main goal of this work is to study a fourth-order parabolic equation with nonstandard growth conditions. For non-positive initial energy J ( u 0 ) ≤ 0 , by using the concavity method, we establish that weak solutions blow up in finite time. On the other hand, we also derive the blow-up time estimate and the asymptotic behavior of weak solutions.

Authors:A.G. Ramm Pages: 1 - 5 Abstract: Publication date: March 2018 Source:Applied Mathematics Letters, Volume 77 Author(s): A.G. Ramm P. Novikov in 1938 has proved that if u 1 ( x ) = u 2 ( x ) for x > R , where R > 0 is a large number, u j ( x ) ≔ ∫ D j g 0 ( x , y ) d y , g 0 ( x , y ) ≔ 1 4 π x − y , and D j ⊂ R 3 , j = 1 , 2 , D j ⊂ B R , are bounded, connected, smooth domains, star-shaped with respect to a common point, then D 1 = D 2 . Here B R ≔ { x : x ≤ R } . Our basic results are: (a) the removal of the assumption about star-shapeness of D j , (b) a new approach to the problem, (c) the construction of counter-examples for a similar problem in which g 0 is replaced by g = e i k x − y 4 π x − y , where k > 0 is a fixed constant.

Authors:M.J. Park; O.M. Kwon; J.H. Ryu Pages: 6 - 12 Abstract: Publication date: March 2018 Source:Applied Mathematics Letters, Volume 77 Author(s): M.J. Park, O.M. Kwon, J.H. Ryu This paper investigates a stability problem for linear systems with time-delay. By constructing simple Lyapunov–Krasovskii functional (LKF), and utilizing a new generalized integral inequality (GII) proposed in this paper, a sufficient stability condition for the systems will be derived in terms of linear matrix inequalities (LMIs). Two illustrative examples are given to show the superiorities of the proposed criterion.

Authors:Wenjun Cui; Lijia Han Pages: 13 - 20 Abstract: Publication date: March 2018 Source:Applied Mathematics Letters, Volume 77 Author(s): Wenjun Cui, Lijia Han This paper is devoted to the study of the infinite propagation speed and the asymptotic behavior for a generalized Camassa–Holm equation with cubic nonlinearity. First, we get the infinite propagation speed in the sense that the corresponding solution with compactly supported initial data does not have compact support any longer in its lifespan. Then, the asymptotic behavior of the solution at infinity is investigated. Especially, we prove that the solution decays algebraically with the same exponent as that of the initial data.

Authors:Yanbing Yang; Runzhang Xu Pages: 21 - 26 Abstract: Publication date: March 2018 Source:Applied Mathematics Letters, Volume 77 Author(s): Yanbing Yang, Runzhang Xu This paper is concerned with the finite time blow up of the solution to the Cauchy problem for the Klein–Gordon equation at arbitrarily positive initial energy level. By introducing a new auxiliary function and an adapted concavity method we establish some sufficient conditions on initial data such that the solution blows up in finite time, which extends the results established in Wang (2008).

Authors:Zhong Tan; Wenpei Wu; Jianfeng Zhou Pages: 27 - 34 Abstract: Publication date: March 2018 Source:Applied Mathematics Letters, Volume 77 Author(s): Zhong Tan, Wenpei Wu, Jianfeng Zhou In this paper, we consider the incompressible magneto-hydro-dynamic equations in the whole space. We first show that there exist global mild solutions with small initial data in the scaling invariant space. The main technique we have used is implicit function theorem which yields necessarily continuous dependence of solutions for the initial data. Moreover, we gain the asymptotic stability of solutions as the time goes to infinity. Finally, as a byproduct of our construction of solutions in the weak L p -spaces, the existence of self-similar solutions was established provided the initial data are small homogeneous functions.

Authors:Chun Shen Pages: 35 - 43 Abstract: Publication date: March 2018 Source:Applied Mathematics Letters, Volume 77 Author(s): Chun Shen The Riemann solutions for a symmetric Keyfitz–Kranzer system are constructed explicitly, in which some singular hyperbolic waves are discovered such as the delta shock wave and the composite wave J R . The global solutions to the double Riemann problem are achieved when the delta shock wave is involved. It is shown that a delta shock wave is separated into a delta contact discontinuity and a shock wave during the process of constructing solutions.

Authors:Vladimir Mityushev Pages: 44 - 48 Abstract: Publication date: March 2018 Source:Applied Mathematics Letters, Volume 77 Author(s): Vladimir Mityushev Extensions of Maxwell’s self-consistent approach from single- to n - inclusions problems lead to cluster methods applied to computation of the effective properties of composites. We describe applications of Maxwell’s formalism to finite clusters and explain the uncertainty arising when n tends to infinity by study of the corresponding conditionally convergent series.

Authors:F.Z. Geng; S.P. Qian Pages: 49 - 56 Abstract: Publication date: March 2018 Source:Applied Mathematics Letters, Volume 77 Author(s): F.Z. Geng, S.P. Qian Based on the piecewise polynomial reproducing kernels, the authors presented the reproducing kernel method(RKM) for nonlocal boundary value problems. In this paper, we will present an optimal RKM for linear nonlocal boundary value problems by combining the piecewise polynomial kernel with polynomial kernel. The method is of high accuracy. Also, the method can avoid reducing the inhomogeneous boundary conditions to homogeneous boundary conditions and constructing reproducing kernel satisfying corresponding homogeneous boundary conditions. Numerical examples are included to demonstrate the validity of the new method.

Abstract: Publication date: May 2018 Source:Applied Mathematics Letters, Volume 79 Author(s): Li Ma In this paper, we investigate a two-cooperative species model with reaction cross-diffusion under the Dirichlet boundary value condition. By applying Lyapunov–Schmidt reduction method and some important formulas, we obtain the existence of coexistence solutions under some given conditions.

Authors:Lei Qiao Abstract: Publication date: April 2018 Source:Applied Mathematics Letters, Volume 78 Author(s): Lei Qiao In this paper, we prove a general Phragmén–Lindelöf principle for weak solutions of the Schrödinger equation in unbounded domains (open, connected sets) in R n ( n ≥ 2 ) . As applications, we shall show some similar results, including the Phragmén–Lindelöf principle for solutions of the Schrödinger equation in a cylinder, can be obtained as special cases of the general result.

Authors:Jun Zhou Abstract: Publication date: April 2018 Source:Applied Mathematics Letters, Volume 78 Author(s): Jun Zhou We consider a nonlocal parabolic equation. By exploiting the boundary condition and the variational structure of the equation, we prove finite time blow-up of the solution for initial data at arbitrary energy level. We also obtain the lifespan of the blow-up solution. The results generalize the former studies on this equation.