Abstract: Publication date: June 2018 Source:Applied Mathematics Letters, Volume 80 Author(s): Junxiong Jia, Bangyu Wu This paper is concerned with Carleman estimates for some anisotropic space-fractional diffusion equations, which are important tools for investigating the corresponding control and inverse problems. By employing a special weight function and the nonlocal vector calculus, we prove a Carleman estimate and apply it to build a stability result for a backward diffusion problem.

Abstract: Publication date: June 2018 Source:Applied Mathematics Letters, Volume 80 Author(s): Jishan Fan, Bessem Samet, Yong Zhou In this paper, we first prove global well-posedness of weak solutions for an epitaxial growth model with L 2 initial data in any dimension d . Then, we establish a regularity criterion of strong solutions with dimension d ≥ 3 .

Abstract: Publication date: June 2018 Source:Applied Mathematics Letters, Volume 80 Author(s): Xingqiu Zhang, Qiuyan Zhong In this paper, different height functions of the nonlinear term on special bounded sets together with Leggett–Williams and Krasnosel’skii fixed point theorems are employed to establish the existence of triple positive solutions for a class of higher-order fractional differential equations with integral conditions. The singularities are with respect not only to the time but also to the space variables.

Abstract: Publication date: June 2018 Source:Applied Mathematics Letters, Volume 80 Author(s): Sun-Hye Park, Mi Jin Lee, Jum-Ran Kang In this work we consider a viscoelastic wave equation of the form u t t − Δ u + ∫ 0 t g ( t − s ) Δ u ( s ) d s + h ( u t ) = u p − 2 u with Dirichlet boundary condition. There are much literature on the blow-up result of solutions for the wave equation with damping term having polynomial growth near zero. However, to my knowledge, there is no blow-up result of solutions for the viscoelastic wave equation without polynomial growth near zero assumption on the damping term. This work is devoted to study a finite time blow-up result of solution with nonpositive initial energy as well as positive initial energy without imposing any restrictive growth near zero assumption on the damping term.

Abstract: Publication date: June 2018 Source:Applied Mathematics Letters, Volume 80 Author(s): Yulei Cao, Jiguang Rao, Dumitru Mihalache, Jingsong He The ( 2 + 1 ) -dimensional [ ( 2 + 1 ) d ] Fokas system is a natural and simple extension of the nonlinear Schrödinger equation (see Eq. (2) in Fokas, 1994). In this letter, we introduce its PT -symmetric version, which is called the ( 2 + 1 ) d nonlocal Fokas system. The N -soliton solutions for this system are obtained by using the Hirota bilinear method whereas the semi-rational solutions are generated by taking the long-wave limit of a part of exponential functions in the general expression of the N -soliton solution. Three kinds of semi-rational solutions, namely (1) a hybrid of rogue waves and periodic line waves, (2) a hybrid of lump and breather solutions, and (3) a hybrid of lump, breather, and periodic line waves are put forward and their rather complicated dynamics is revealed.

Abstract: Publication date: June 2018 Source:Applied Mathematics Letters, Volume 80 Author(s): Alexander Zlotnik, Raimondas Čiegis The stability bounds and error estimates for a compact higher order Numerov–Crank–Nicolson scheme on non-uniform spatial meshes for the 1D time-dependent Schrödinger equation have been recently derived. This analysis has been done in L 2 and H 1 mesh norms and used the non-standard “converse” condition h ω ≤ c 0 τ , where h ω is the mean spatial step, τ is the time step and c 0 > 0 . Now we prove that such condition is necessary for some families of non-uniform meshes and any spatial norm. Also computational results for zero and non-zero potentials show unacceptably wrong behavior of numerical solutions when τ decreases and this condition is violated.

Abstract: Publication date: June 2018 Source:Applied Mathematics Letters, Volume 80 Author(s): Yu Ping Wang, V.A. Yurko The inverse spectral problem for Dirac operators is studied. By using the result on the Weyl m -function, we show that the Hochstadt–Lieberman-type and Borg-type theorem for Dirac operators except for one arbitrary eigenvalue hold.

Abstract: Publication date: June 2018 Source:Applied Mathematics Letters, Volume 80 Author(s): Xi-Yang Xie, Ze-Hui Yan Under investigation in this paper is a Kundu–Eckhaus equation with variable coefficients, which models the propagation of the ultra-short femtosecond pulses in an optical fiber. Bright one- and two-soliton solutions for this equation are constructed, based on the bilinear forms obtained. Then, by the aid of the solutions, propagation of the one solitons and collisions between the two solitons are illustrated in figures, and with the help of the asymptotic analysis on the two-soliton solutions, the collisions are proved to be elastic. Influences of r ( x ) and m ( x ) on the solitons are also be analyzed, where r ( x ) and m ( x ) are respectively the group velocity dispersion and nonlinearity parameter: When they are both chosen as the constants, it can be found that the one solitons propagate with unvarying velocities and amplitudes, and shapes of the two solitons are maintained before and after the collisions; r ( x ) and m ( x ) are found to affect the velocities and amplitudes of the solitons, respectively.

Abstract: Publication date: June 2018 Source:Applied Mathematics Letters, Volume 80 Author(s): Xiaowei An, Zhen He, Xianfa Song Using the solutions of an elliptic system and an ODE system, under certain conditions, we get the explicit solution to the following initial–boundary value problem of Gierer-Meinhardt model u t = d 1 Δ u − a 1 u + u p v q + δ 1 ( x , t ) , x ∈ Ω , t > 0 v t = d 2 Δ v − a 2 v + u r v s + δ 2 ( x , t ) , x ∈ Ω , t > 0 ∂ u ∂ η = ∂ v ∂ η = 0 ( or u = v = 0 ) , x ∈ ∂ Ω , t > 0 u ( x , 0 ) = u 0 ( x ) , v ( x , 0 ) = v 0 ( x ) , x ∈ Ω . Here p > 1 , s > − 1 , d 1 , d 2 , q , r > 0 and a 1 , a 2 ≥ 0 are constants, while δ 1 ( x , t ) and δ 2 ( x , t ) are nonnegative continuous functions.

Abstract: Publication date: June 2018 Source:Applied Mathematics Letters, Volume 80 Author(s): Yunfeng Jia We consider a reaction–diffusion population model with predator–prey-dependent functional response. Firstly, we discuss the conditions which ensure the model has a unique positive constant solution. Secondly, we investigate the dynamical properties of the model, including the large time behaviors of the nonconstant solutions and the local and the global asymptotic stability of the positive constant solution.

Abstract: Publication date: May 2018 Source:Applied Mathematics Letters, Volume 79 Author(s): Chein-Shan Liu, Jiang-Ren Chang An inverse source problem for the recovery of an unknown space–time dependent source term of a time-fractional Burgers equation is solved in the paper. By using the prescribed boundary data, a sequence of boundary functions is derived, which together with the zero element constitute a linear space. An energy boundary functional equation is derived in the linear space, of which the time-dependent energy is preserved for each energy boundary function. The iterative algorithm used to recover the unknown source with energy boundary functions as the bases is developed, which is robust and convergent fast.

Abstract: Publication date: May 2018 Source:Applied Mathematics Letters, Volume 79 Author(s): Jitsuro Sugie, Kazuki Ishibashi The purpose of this paper is to provide an oscillation theorem that can be applied to half-linear differential equations with time-varying coefficients. A parametric curve by the coefficients is focused in order to obtain our theorem. This parametric curve is a generalization of the curve given by the characteristic equation of the second-order linear differential equation with constant coefficients. The obtained theorem is proved by transforming the half-linear differential equation to a standard polar coordinates system and using phase plane analysis carefully.

Abstract: Publication date: May 2018 Source:Applied Mathematics Letters, Volume 79 Author(s): Jian-Guo Liu, Yu Tian, Jian-Guo Hu The ( G ′ ∕ G ) -expansion approach is an efficient and well-developed approach to solve nonlinear partial differential equations. In this paper, the (3+1)-dimensional Boiti–Leon–Manna–Pempinelli equation is investigated by using this approach, which describes the (2+1)-dimensional interaction of the Riemann wave propagated along the y -axis with a long wave propagated along the x -axis and can be considered as a model for the incompressible fluid. With the aid of symbolic computation, a family of exact solutions are obtained in forms of the hyperbolic functions and the trigonometric functions. When the parameters are selected special values, non-traveling wave solutions are also presented, and these gained solutions have abundant structures. The figures corresponding to these solutions are illustrated to show the particular localized excitations and the interactions between two solitary waves.

Abstract: Publication date: May 2018 Source:Applied Mathematics Letters, Volume 79 Author(s): Won-Kwang Park Various studies have confirmed the possibility of identifying the location of a set of small inhomogeneities via a direct sampling method; however, when their permeability differs from that of the background, their location cannot be satisfactorily identified. However, no theoretical explanation for this phenomenon has been verified. In this study, we demonstrate that the indicator function of the direct sampling method can be expressed by the Bessel function of order one of the first kind and explain why the exact locations of inhomogeneities cannot be identified. Numerical results with noisy data are exhibited to support our examination.

Abstract: Publication date: May 2018 Source:Applied Mathematics Letters, Volume 79 Author(s): Hongliang Liu, Zhisu Liu, Qizhen Xiao In this paper, we study the existence of ground state solutions of nonlinear elliptic equation with logarithmic nonlinearity by the Linking theorem and logarithmic Sobolev inequality. Our results are quite different from those in the case of polynomial nonlinearity.

Abstract: Publication date: May 2018 Source:Applied Mathematics Letters, Volume 79 Author(s): Da-Wei Zuo Nonlinear Schrödinger Maxwell–Bloch equation with a perturbation has been discussed in this paper. By virtue of the Darboux transformation and Joukowsky transformation, three kinds of N -order breathers have been attained. Propagation and interaction of the breathers have been obtained: spectrum parameter determined the types of the breathers; spectrum parameter has affect on the breathers synchronization/asynchronization; breather asynchronization is consistent with theories for relations of modulation instability and rogue waves; Modulation instability has also been discussed.

Abstract: Publication date: May 2018 Source:Applied Mathematics Letters, Volume 79 Author(s): Chein-Shan Liu, Fajie Wang, Yan Gu The inverse Cauchy problem of Laplace equation is hard to solve numerically, since it is highly ill-posed in the Hadamard sense. With this in mind, we propose a natural regularization technique to overcome the difficulty. In the linear space of the Trefftz bases for solving the Laplace equation, we introduce a novel concept to construct the Trefftz energy bases used in the numerical solution for the inverse Cauchy problem of the Laplace equation in arbitrary star plane domain. The Trefftz energy bases not only satisfy the Laplace equation but also preserve the energy, whose performance is better than the original Trefftz bases. We test the new method by two numerical examples.

Abstract: Publication date: May 2018 Source:Applied Mathematics Letters, Volume 79 Author(s): Klemens Fellner, Michael Kniely We consider a Shockley–Read–Hall recombination–drift–diffusion model coupled to Poisson’s equation and subject to boundary conditions, which imply conservation of the total charge. As main result, we derive an explicit functional inequality between relative entropy and entropy production rate, which implies exponential convergence to equilibrium with explicit constant and rate. We report that the key entropy–entropy production inequality ought rather not to be formulated on the states space of the parabolic–elliptic system, but on the reduced states space of the associated nonlocal drift–diffusion problem, where the Poisson equation is replaced by the corresponding Green function.

Abstract: Publication date: May 2018 Source:Applied Mathematics Letters, Volume 79 Author(s): Deng-Shan Wang, Jiang Liu Some two-component Korteweg–de Vries systems are studied by prolongation technique and Painlevé analysis. Especially, the two-component KdV system conjectured to be integrable by Foursov is proved to be both Lax integrable and P-integrable. Its conservation laws are investigated based on the obtained Lax pair. Furthermore, it is shown that the three two-component Korteweg–de Vries systems are identical under certain invertible linear transformations. Finally, the auto-Bäcklund transformation and some exact solutions for the two-component Korteweg–de Vries system are derived explicitly.

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.

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.