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2017年, 第37卷, 第4期　刊出日期：2017-08-25 上一期    下一期

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RENORMALIZED SOLUTIONS OF ELLIPTIC EQUATIONS WITH ROBIN BOUNDARY CONDITIONS Olivier GUIBÉ, Alip OROPEZA 数学物理学报(英文版). 2017 (4):  889-910.  DOI: 10.1016/S0252-9602(17)30046-2 摘要 ( 98 )   RICH HTML PDF   收藏 In the present paper, we consider elliptic equations with nonlinear and nonhomogeneous Robin boundary conditions of the type where f and g are the element of L1(Ω) and L1(Γ1), respectively. We define a notion of renormalized solution and we prove the existence of a solution. Under additional assumptions on the matrix field B we show that the renormalized solution is unique. 参考文献 | 相关文章 | 计量指标

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EXISTENCE OF SOLUTIONS OF NONLOCAL PERTURBATIONS OF DIRICHLET DISCRETE NONLINEAR PROBLEMS Alberto CABADA, Nikolay D. DIMITROV 数学物理学报(英文版). 2017 (4):  911-926.  DOI: 10.1016/S0252-9602(17)30047-4 摘要 ( 84 )   RICH HTML PDF   收藏 This paper is devoted to the study of second order nonlinear difference equations. A Nonlocal Perturbation of a Dirichlet Boundary Value Problem is considered. An exhaustive study of the related Green's function to the linear part is done. The exact expression of the function is given, moreover the range of parameter for which it has constant sign is obtained. Using this, some existence results for the nonlinear problem are deduced from monotone iterative techniques, the classical Krasnoselski fixed point theorem or by application of recent fixed point theorems that combine both theories. 参考文献 | 相关文章 | 计量指标

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DYNAMICAL BEHAVIOR OF A STOCHASTIC HBV INFECTION MODEL WITH LOGISTIC HEPATOCYTE GROWTH 刘群, 蒋达清, 史宁中, Tasawar HAYAT, Ahmed ALSAEDI 数学物理学报(英文版). 2017 (4):  927-940.  DOI: 10.1016/S0252-9602(17)30048-6 摘要 ( 108 )   RICH HTML PDF   收藏 This paper is concerned with a stochastic HBV infection model with logistic growth. First, by constructing suitable stochastic Lyapunov functions, we establish sufficient conditions for the existence of ergodic stationary distribution of the solution to the HBV infection model. Then we obtain sufficient conditions for extinction of the disease. The stationary distribution shows that the disease can become persistent in vivo. 参考文献 | 相关文章 | 计量指标

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GLOBAL WELL-POSEDNESS AND BLOW-UP FOR THE HARTREE EQUATION 杨凌燕, 李晓光, 吴永洪, Louis CACCETTA 数学物理学报(英文版). 2017 (4):  941-948.  DOI: 10.1016/S0252-9602(17)30049-8 摘要 ( 80 )   RICH HTML PDF   收藏 For 2 < γ < min{4, n}, we consider the focusing Hartree equation iut + △u + (|x|-γ *|u|2)u=0, x ∈ Rn. (0.1) Let M[u] and E[u] denote the mass and energy, respectively, of a solution u, and Q be the ground state of -△ Q + Q=(|x|-γ *|Q|2)Q. Guo and Wang[Z. Angew. Math. Phy.,2014] established a dichotomy for scattering versus blow-up for the Cauchy problem of (0.1) if M[u]1-scE[u]sc < M[Q]1-scE[Q]sc(sc=γ-2/2). In this paper, we consider the complementary case M[u]1-scE[u]sc ≥ M[Q]1-scE[Q]sc and obtain a criteria on blow-up and global existence for the Hartree equation (0.1). 参考文献 | 相关文章 | 计量指标

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ON THE GLOBAL EXISTENCE OF SMOOTH SOLUTIONS TO THE MULTI-DIMENSIONAL COMPRESSIBLE EULER EQUATIONS WITH TIME-DEPENDING DAMPING IN HALF SPACE 侯飞 数学物理学报(英文版). 2017 (4):  949-964.  DOI: 10.1016/S0252-9602(17)30050-4 摘要 ( 53 )   RICH HTML PDF   收藏 This paper is a continue work of[4, 5]. In the previous two papers, we studied the Cauchy problem of the multi-dimensional compressible Euler equations with time-depending damping term -(μ/(1+t)λ)ρu, where λ ≥ 0 and μ > 0 are constants. We have showed that, for all λ ≥ 0 and μ > 0, the smooth solution to the Cauchy problem exists globally or blows up in finite time. In the present paper, instead of the Cauchy problem we consider the initialboundary value problem in the half space R+d with space dimension d=2, 3. With the help of the special structure of the equations and the fluid vorticity, we overcome the difficulty arisen from the boundary effect. We prove that there exists a global smooth solution for 0 ≤ λ < 1 when the initial data is close to its equilibrium state. In addition, exponential decay of the fluid vorticity will also be established. 参考文献 | 相关文章 | 计量指标

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STABILITY OF A VON KARMAN EQUATION WITH INFINITE MEMORY Sun-Hye PARK 数学物理学报(英文版). 2017 (4):  965-973.  DOI: 10.1016/S0252-9602(17)30051-6 摘要 ( 73 )   RICH HTML PDF   收藏 In this paper, we consider a von Karman equation with infinite memory. For von Karman equations with finite memory, there is a lot of literature concerning on existence of the solutions, decay of the energy, and existence of the attractors. However, there are few results on existence and energy decay rate of the solutions for von Karman equations with infinite memory. The main goal of the present paper is to generalize previous results by treating infinite history instead of finite history. 参考文献 | 相关文章 | 计量指标

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BLOW-UP AND LIFE SPAN ESTIMATES FOR A CLASS OF NONLINEAR DEGENERATE PARABOLIC SYSTEM WITH TIME-DEPENDENT COEFFICIENTS 夏安银, 樊明书, 李珊 数学物理学报(英文版). 2017 (4):  974-984.  DOI: 10.1016/S0252-9602(17)30052-8 摘要 ( 69 )   RICH HTML PDF   收藏 This paper deals with the singularity and global regularity for a class of nonlinear porous medium system with time-dependent coefficients under homogeneous Dirichlet boundary conditions. First, by comparison principle, some global regularity results are established. Secondly, using some differential inequality technique, we investigate the blow-up solution to the initial-boundary value problem. Furthermore, upper and lower bounds for the maximum blow-up time under some appropriate hypotheses are derived as long as blow-up occurs. 参考文献 | 相关文章 | 计量指标

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IMPULSIVE DIFFERENTIAL EQUATIONS WITH GAMMA DISTRIBUTED MOMENTS OF IMPULSES AND P-MOMENT EXPONENTIAL STABILITY R. AGARWAL, S. HRISTOVA, P. KOPANOV, D. O'REGAN 数学物理学报(英文版). 2017 (4):  985-997.  DOI: 10.1016/S0252-9602(17)30053-X 摘要 ( 98 )   RICH HTML PDF   收藏 Differential equations with impulses at random moments are set up and investigated. We study the case of Gamma distributed random moments of impulses. Several properties of solutions are studied based on properties of Gammma distributions. Some sufficient conditions for p-moment exponential stability of the solutions are given. 参考文献 | 相关文章 | 计量指标

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ORBITAL STABILITY OF PERIODIC TRAVELING WAVE SOLUTIONS TO THE GENERALIZED ZAKHAROV EQUATIONS 郑筱筱, 尚亚东, 彭小明 数学物理学报(英文版). 2017 (4):  998-1018.  DOI: 10.1016/S0252-9602(17)30054-1 摘要 ( 113 )   RICH HTML PDF   收藏 This paper investigates the orbital stability of periodic traveling wave solutions to the generalized Zakharov equations First, we prove the existence of a smooth curve of positive traveling wave solutions of dnoidal type with a fixed fundamental period L for the generalized Zakharov equations. Then, by using the classical method proposed by Benjamin, Bona et al., we show that this solution is orbitally stable by perturbations with period L. The results on the orbital stability of periodic traveling wave solutions for the generalized Zakharov equations in this paper can be regarded as a perfect extension of the results of[15, 16, 19]. 参考文献 | 相关文章 | 计量指标

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CONDITIONAL EXPECTATIONS AND MARTINGALES IN NONCOMMUTATIVE Lp-SPACES ASSOCIATED WITH CENTER-VALUED TRACES Inomjon GANIEV, Farrukh MUKHAMEDOV 数学物理学报(英文版). 2017 (4):  1019-1032.  DOI: 10.1016/S0252-9602(17)30055-3 摘要 ( 83 )   RICH HTML PDF   收藏 In this paper we prove the existence of conditional expectations in the noncommutative Lp(M, Φ)-spaces associated with center-valued traces. Moreover, their description is also provided. As an application of the obtained results, we establish the norm convergence of weighted averages of martingales in noncommutative Lp(M, Φ)-spaces. 参考文献 | 相关文章 | 计量指标

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LOCAL REGULARITY CRITERIA OF A SUITABLE WEAK SOLUTION TO MHD EQUATIONS Jae-Myoung KIM 数学物理学报(英文版). 2017 (4):  1033-1047.  DOI: 10.1016/S0252-9602(17)30056-5 摘要 ( 108 )   RICH HTML PDF   收藏 We present a regularity condition of a suitable weak solution to the MHD equations in three dimensional space with slip boundary conditions for a velocity and magnetic vector fields. More precisely, we prove a suitable weak solution are Hölder continuous near boundary provided that the scaled mixed Lx,tp,q -norm of the velocity vector field with 3/p + 2/q ≤ 2, 2 < q < ∞ is sufficiently small near the boundary. Also, we will investigate that for this solution u ∈ Lx,tp,q with 1 ≤ 3/p + 2/q ≤ 3/2, 3 < p < ∞, the Hausdorff dimension of its singular set is no greater than max{p,q}(3/p + 2/q -1). 参考文献 | 相关文章 | 计量指标

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ANALYSIS OF AN ELASTO-PIEZOELECTRIC SYSTEM OF HEMIVARIATIONAL INEQUALITIES WITH THERMAL EFFECTS Paweł SZAFRANIEC 数学物理学报(英文版). 2017 (4):  1048-1060.  DOI: 10.1016/S0252-9602(17)30057-7 摘要 ( 91 )   RICH HTML PDF   收藏 In this paper we prove the existence and uniqueness of a weak solution for a dynamic electo-viscoelastic problem that describes a contact between a body and a foundation. We assume the body is made from thermoviscoelastic material and consider nonmonotone boundary conditions for the contact.We use recent results from the theory of hemivariational inequalities and the fixed point theory. 参考文献 | 相关文章 | 计量指标

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SHARP WELL-POSEDNESS OF THE CAUCHY PROBLEM FOR THE HIGHER-ORDER DISPERSIVE EQUATION 蒋敏杰, 闫威, 张贻民 数学物理学报(英文版). 2017 (4):  1061-1082.  DOI: 10.1016/S0252-9602(17)30058-9 摘要 ( 51 )   RICH HTML PDF   收藏 This current paper is devoted to the Cauchy problem for higher order dispersive equation ut + ∂x2n+1u=∂x(u∂xnu) + ∂xn-1(ux2), n ≥ 2, n ∈ N+. By using Besov-type spaces, we prove that the associated problem is locally well-posed in H(-n/2 + 3/4,-1/2n)(R). The new ingredient is that we establish some new dyadic bilinear estimates. When n is even, we also prove that the associated equation is ill-posed in H(s,a)(R) with s < -n/2 + 3/4 and all a ∈ R. 参考文献 | 相关文章 | 计量指标

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DUALITY OF WEIGHTED MULTIPARAMETER TRIEBEL-LIZORKIN SPACES 丁卫, 朱月萍 数学物理学报(英文版). 2017 (4):  1083-1104.  DOI: 10.1016/S0252-9602(17)30059-0 摘要 ( 61 )   RICH HTML PDF   收藏 In this paper, we reintroduce the weighted multi-parameter Triebel-Lizorkin spaces ?pα,q(ω; Rn1×Rn2) based on the Frazier and Jawerth' method in[11]. This space was firstly introduced in[18]. Then we establish its dual space and get that (?pα,q)*=CMOp-α,q' for 0 < p ≤ 1. 参考文献 | 相关文章 | 计量指标

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LEGENDRE SPECTRAL COLLOCATION METHOD FOR VOLTERRA-HAMMERSTEIN INTEGRAL EQUATION OF THE SECOND KIND 魏云霞, 陈艳萍 数学物理学报(英文版). 2017 (4):  1105-1114.  DOI: 10.1016/S0252-9602(17)30060-7 摘要 ( 62 )   RICH HTML PDF   收藏 This paper is concerned with obtaining the approximate solution for VolterraHammerstein integral equation with a regular kernel. We choose the Gauss points associated with the Legendre weight function ω(x)=1 as the collocation points. The Legendre collocation discretization is proposed for Volterra-Hammerstein integral equation. We provide an error analysis which justifies that the errors of approximate solution decay exponentially in L2 norm and L∞ norm. We give two numerical examples in order to illustrate the validity of the proposed Legendre spectral collocation method. 参考文献 | 相关文章 | 计量指标

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GEVREY REGULARITY WITH WEIGHT FOR INCOMPRESSIBLE EULER EQUATION IN THE HALF PLANE 程峰, 李维喜, 徐超江 数学物理学报(英文版). 2017 (4):  1115-1132.  DOI: 10.1016/S0252-9602(17)30061-9 摘要 ( 74 )   RICH HTML PDF   收藏 In this work we prove the weighted Gevrey regularity of solutions to the incompressible Euler equation with initial data decaying polynomially at infinity. This is motivated by the well-posedness problem of vertical boundary layer equation for fast rotating fluid. The method presented here is based on the basic weighted L2-estimate, and the main difficulty arises from the estimate on the pressure term due to the appearance of weight function. 参考文献 | 相关文章 | 计量指标

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OPTIMALITY CONDITIONS AND DUALITY RESULTS FOR NONSMOOTH VECTOR OPTIMIZATION PROBLEMS WITH THE MULTIPLE INTERVAL-VALUED OBJECTIVE FUNCTION Tadeusz ANTCZAK 数学物理学报(英文版). 2017 (4):  1133-1150.  DOI: 10.1016/S0252-9602(17)30062-0 摘要 ( 58 )   RICH HTML PDF   收藏 In this paper, both Fritz John and Karush-Kuhn-Tucker necessary optimality conditions are established for a (weakly) LU-efficient solution in the considered nonsmooth multiobjective programming problem with the multiple interval-objective function. Further, the sufficient optimality conditions for a (weakly) LU-efficient solution and several duality results in Mond-Weir sense are proved under assumptions that the functions constituting the considered nondifferentiable multiobjective programming problem with the multiple intervalobjective function are convex. 参考文献 | 相关文章 | 计量指标

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MÖBIUS-TODA HIERARCHY AND ITS INTEGRABILITY 李传忠 数学物理学报(英文版). 2017 (4):  1151-1161.  DOI: 10.1016/S0252-9602(17)30063-2 摘要 ( 81 )   RICH HTML PDF   收藏 In this paper, we construct a new integrable equation called Möbius-Toda equation which is a generalization of q-Toda equation. Meanwhile its soliton solutions are constructed to show its integrable property. Further the Lax pairs of the Möbius-Toda equation and a whole integrable Möbius-Toda hierarchy are also constructed. To show the integrability, the bi-Hamiltonian structure and tau symmetry of the Möbius-Toda hierarchy are given and this leads to the existence of the tau function. 参考文献 | 相关文章 | 计量指标

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ON THE FIRST EIGENVALUE OF THE MEAN FINSLER-LAPLACIAN 贺群, 曾凡奇, 郑大小 数学物理学报(英文版). 2017 (4):  1162-1172.  DOI: 10.1016/S0252-9602(17)30064-4 摘要 ( 81 )   RICH HTML PDF   收藏 In this paper, we prove that several different definitions of the Finsler-Laplacian are equivalent. Then we prove that any Berwald metric is affinely equivalent to its mean metric and give some upper or lower bound estimates for the first eigenvalue of the mean Laplacian on Berwald manifolds, which generalize some results in Riemannian geometry. 参考文献 | 相关文章 | 计量指标

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ERRATUM TO:LEAST SQUARES ESTIMATION FOR ORNSTEIN-UHLENBECK PROCESSES DRIVEN BY THE WEIGHTED FRACTIONAL BROWNIAN MOTION 申广君, 尹修伟, 闫理坦 数学物理学报(英文版). 2017 (4):  1173-1176.  DOI: 10.1016/S0252-9602(17)30065-6 摘要 ( 70 )   RICH HTML PDF   收藏 We give a correction of Theorem 2.2 of Shen, Yin and Yan (2016). 参考文献 | 相关文章 | 计量指标