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2010年, 第30卷, 第6期　刊出日期：2010-11-20 上一期    下一期

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CHERISHING THE MEMORY OF ACADEMICIAN LI GUOPING (LEE KOWK-PING) 范文涛, 刘培德, 欧阳才衡 数学物理学报(英文版). 2010 (6):  1837-1844.  DOI: 10.1016/S0252-9602(10)60176-2 摘要 ( 655 )   RICH HTML PDF(119KB) ( 1108 )   收藏 November 15, 2010 is the memorial day of the 100th anniversary of Academician Li Guoping's birthday. We studied under guidance of Professor Li for decades and learnt a lot from his instruction. Like life-giving spring breeze and rain, we have been benefiting from Teacher Li for a lifetime. It has been fourteen years since Professor Li passed away, his voice and expression, personality and charm still often appear in our mind. On the occasion of the 100th anniversary of our teacher's birthday, we contribute this article to memorize dear Teacher Li deeply. 相关文章 | 计量指标

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WU XINMOU(OU SING-MO): IN COMMEMORATION OF THE 100th ANNIVERSARY OF HIS BIRTH 李文林, 陆柱家 数学物理学报(英文版). 2010 (6):  1845-1850.  DOI: 10.1016/S0252-9602(10)60177-4 摘要 ( 680 )   RICH HTML PDF(132KB) ( 1354 )   收藏 Wu Xinmou (Ou Sing-mo) was born in Jiangyin, a peaceful Chinese town in Jiangsu Province by the Yangtze River, on April 14 of 1910, his father was a teacher of history at a local school. Wu Xinmou received his school education in home town and entered the department of mathematics of National Central University in Nanjing where he was taught higher algebra, geometry and analysis by Professor He Lu, a French returned scholar. Having graduated from the Central University in 1932, Wu Xinmou taught at the department of mathematics as an assistant professor in Tsinghua University from 1934 to 1937, and became interested in differential equations under the influence of Professor Xiong Qinglai (Hiong King-lai), who owned French Doctorat d'Etat and  chaired the department from 1928 to 1937. Wu was sent to France at state expense in 1937, where he took at first H. Villat's class in viscous fluid mechanics and changed eventually his major to partial differential equations supervised by J. Hadamard. During his stay in France, as well as intensive academic researches, Wu Xinmou took part in the patriotic activities against Japanese invasion led by Chinese Communist Party, in particular he was editor of the journal Anti-Japanese News from Homeland since 1939.  Wu joined Chinese Communist Party as a member of the branch sojourned in France led by Deng Fa and Liu Ning-Yi in 1945. 参考文献 | 相关文章 | 计量指标

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A BLOW-UP CRITERION FOR COMPRESSIBLE VISCOUS HEAT-CONDUCTIVE FLOWS 江松, 欧耀彬 数学物理学报(英文版). 2010 (6):  1851-1864.  DOI: 10.1016/S0252-9602(10)60178-6 摘要 ( 1000 )   RICH HTML PDF(192KB) ( 1346 )   收藏 We study an initial boundary value problem for the Navier-Stokes equations of compressible viscous heat-conductive fluids in a 2-D periodic domain or the unit square domain. We establish a blow-up criterion for the local strong solutions in terms of the gradient of the velocity only, which coincides with the famous Beale-Kato-Majda criterion for ideal incompressible flows. 参考文献 | 相关文章 | 计量指标

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COMPLEXITY OF ASYMPTOTIC BEHAVIOR OF SOLUTIONS FOR THE POROUS MEDIUM EQUATION WITH ABSORPTION 尹景学, 王良伟, 黄锐 数学物理学报(英文版). 2010 (6):  1865-1880.  DOI: 10.1016/S0252-9602(10)60179-8 摘要 ( 1038 )   RICH HTML PDF(224KB) ( 1379 )   收藏 In this paper we analyze the large time behavior of nonnegative solutions of the Cauchy problem of the porous medium equation with absorption ut-Δum+γup=0, where γ≥0, m>1and p>m+2/N. We will show that if γ=0 and 0<μ<2N/N(m-1)+2, or γ>0 and 1/p-1<μ<2N/N(m-1)+2, then for any nonnegative function φ in a nonnegative countable subset F of the Schwartz space S(RN), there exists an initial-value u0∈C(RN) with limx→∞u0(x)=0 such that φ is an ω-limit point of the rescaled solutions t u/2u(t β, t), where β=2-u(m-1)/4. 参考文献 | 相关文章 | 计量指标

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FOUNTAIN THEOREM OVER CONES AND APPLICATIONS 严树森, 杨健夫 数学物理学报(英文版). 2010 (6):  1881-1888.  DOI: 10.1016/S0252-9602(10)60180-4 摘要 ( 661 )   RICH HTML PDF(164KB) ( 1466 )   收藏 In this paper, we establish fountain theorems over cones and apply it to the quasilinear elliptic problem { -Δp u =λ |u|q-2u +μ |u| γ-2u,       x∈Ω,  u = 0,                                             x∈∂Ω,                （1）  to show that problem (1) possesses infinitely many solutions, where 1<p<N, 1< q <p < γ, Ω（RN is a smooth bounded domain and λ，μ∈R. 参考文献 | 相关文章 | 计量指标

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GLOBAL EXISTENCE OF SOLUTIONS FOR ONE-DIMENSIONAL COMPRESSIBLE NAVIER-STOKES EQUATIONS IN THE HALF SPACE 王淑娟, 赵俊宁 数学物理学报(英文版). 2010 (6):  1889-1905.  DOI: 10.1016/S0252-9602(10)60181-6 摘要 ( 942 )   RICH HTML PDF(201KB) ( 1032 )   收藏 We prove the existence of global solutions to the initial-boundary-value problem on the half space R+ for a one-dimensional viscous ideal polytropic gas. Some suitable assumptions are made to guarantee the existence of smooth solutions. Employing the L2-energy estimate, we prove that the impermeable problem has a unique global solutionis. 参考文献 | 相关文章 | 计量指标

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STABILITY OF VISCOUS CONTACT WAVE FOR COMPRESSIBLE NAVIER-STOKES SYSTEM OF GENERAL GAS WITH FREE BOUNDARY 黄飞敏, 王勇, 翟晓云 数学物理学报(英文版). 2010 (6):  1906-1916.  DOI: 10.1016/S0252-9602(10)60182-8 摘要 ( 885 )   RICH HTML PDF(171KB) ( 1329 )   收藏 In this paper, we study the large time behavior  of solutions to the nonisentropic Navier-Stokes equations of general gas, where polytropic gas is included as a special case, with a free boundary. First we construct a viscous contact wave which approximates to the contact discontinuity, which is a basic wave pattern of compressible Euler equation, in finite time as the heat conductivity tends to zero. Then we prove the viscous contact wave is asymptotic stable if the initial perturbations and the strength of the contact wave are small. This generalizes our previous result [6] which is only for polytropic gas. 参考文献 | 相关文章 | 计量指标

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THE EXISTENCE OF NONTRIVIAL SOLUTIONS TO A SEMILINEAR ELLIPTIC SYSTEM ON RN WITHOUT THE AMBROSETTI-RABINOWITZ CONDITION 李工宝, 王春花 数学物理学报(英文版). 2010 (6):  1917-1936.  DOI: 10.1016/S0252-9602(10)60183-X 摘要 ( 920 )   RICH HTML PDF(243KB) ( 1430 )   收藏 In this paper, we prove the existence of at least one positive solution pair (u, v)∈H1(RN)×H1(RN) to the following semilinear elliptic system {-Δu+u=f(x, v),        x∈RN,    -Δv+v=g(x, u),      x∈RN,                      (0.1) by using a linking theorem and the concentration-compactness principle. The main conditions we imposed on the nonnegative functions f, g ∈ C0(RN×R1) are that, f(x, t ) and g(x, t) are superlinear at t=0 as well as at t=+∞, that f and g are subcritical in t and satisfy a kind of monotonic conditions. We mention that we do not assume that f or g satisfies the Ambrosetti-Rabinowitz condition as usual. Our main result can be viewed as an extension to a recent result of Miyagaki and Souto [J. Diff. Equ. 245(2008), 3628-3638] concerning the existence of a positive solution to the semilinear elliptic boundary value problem  {-Δu+u=f(x, u),       x∈Ω,   u∈H10(Ω)  where Ω（RN is bounded and a result of Li and Yang [G. Li and J. Yang: Communications in P.D.E. Vol. 29(2004) Nos.5 & 6.pp.925--954, 2004] concerning (0.1)  when f and g are asymptotically linear. 参考文献 | 相关文章 | 计量指标

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COMPRESSIBLE NAVIER-STOKES-POISSON EQUATIONS 肖玲, 李海梁 数学物理学报(英文版). 2010 (6):  1937-1948.  DOI: 10.1016/S0252-9602(10)60184-1 摘要 ( 1138 )   RICH HTML PDF(192KB) ( 2796 )   收藏 This is a survey paper on the study of compressible Navier-Stokes-Poisson equations. The emphasis is on the long time behavior of global solutions to multi-dimensional compressible Navier-Stokes-Poisson equations, and the optimal decay rates for both unipolar and bipolar compressible Navier-Stokes-Poisson equations are discussed. 参考文献 | 相关文章 | 计量指标

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ON A NEW DEFINITION OF RICCI CURVATURE ON ALEXANDROV SPACES 张会春, 朱熹平 数学物理学报(英文版). 2010 (6):  1949-1974.  DOI: 10.1016/S0252-9602(10)60185-3 摘要 ( 1322 )   RICH HTML PDF(305KB) ( 1511 )   收藏 Recently, in [49], a new definition for lower Ricci curvature bounds on Alexandrov spaces was introduced by the authors. In this article, we  extend our research to summarize the  geometric and analytic results under this Ricci condition. In particular, two new results, the rigidity result of Bishop-Gromov volume    comparison and Lipschitz continuity of heat kernel, are obtained. 参考文献 | 相关文章 | 计量指标

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ELECTRICALLY CHARGED SOLITONS IN GAUGE FIELD THEORY 杨亦松 数学物理学报(英文版). 2010 (6):  1975-2005.  DOI: 10.1016/S0252-9602(10)60186-5 摘要 ( 748 )   RICH HTML PDF(317KB) ( 1397 )   收藏 Monopoles and vortices are well known magnetically charged soliton solutions of gauge field equations. Extending the idea of Dirac on monopoles, Schwinger pioneered the concept of solitons carrying both electric and magnetic charges, called dyons, which are useful in modeling elementary particles. Mathematically, the existence of dyons presents interesting variational partial differential equation problems, subject to topological constraints. This article is a survey on recent progress in the study of dyons. 参考文献 | 相关文章 | 计量指标

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SYMMETRY OF TRANSLATING SOLUTIONS TO MEAN CURVATURE FLOWS 简怀玉, 鞠红杰, 刘艳楠, 孙伟 数学物理学报(英文版). 2010 (6):  2006-2016.  DOI: 10.1016/S0252-9602(10)60187-7 摘要 ( 1443 )   RICH HTML PDF(180KB) ( 1764 )   收藏 First, we review the authors' recent results on translating solutions to mean curvature flows in Euclidean space as well as in Minkowski space, emphasizing on the asymptotic expansion of rotationally symmetric  solutions.  Then we study the sufficient condition  for which  the translating solution is rotationally symmetric. We will use  a moving plane method  to show that this condition is optimal for the symmetry of solutions to fully nonlinear elliptic equations without ground state condition. 参考文献 | 相关文章 | 计量指标

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INFINITELY MANY SOLUTIONS FOR AN ELLIPTIC PROBLEM INVOLVING CRITICAL NONLINEARITY 曹道民, 严树森 数学物理学报(英文版). 2010 (6):  2017-2032.  DOI: 10.1016/S0252-9602(10)60188-9 摘要 ( 876 )   RICH HTML PDF(213KB) ( 1278 )   收藏 We study the following elliptic problem: {−div(a(x)Du) = Q(x)|u|2*-2u+λu      x ∈Ω,   u = 0                                                 on∂Ω. Under certain assumptions on a and Q, we obtain existence of infinitely many solutions by variational method. 参考文献 | 相关文章 | 计量指标

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A RANDOM TRANSPORT-DIFFUSION EQUATION 胡耀忠 数学物理学报(英文版). 2010 (6):  2033-2050.  DOI: 10.1016/S0252-9602(10)60189-0 摘要 ( 760 )   RICH HTML PDF(213KB) ( 1083 )   收藏 In this paper we study the integral curve in a random vector field perturbed by white noise. It is related to a stochastic transport-diffusion equation.  Under some conditions on the covariance  function  of the vector field, the solution of this stochastic partial differential equation is proved to have moments. The exact p-th moment is  represented through integrals with respect to Brownian motions. The basic tool is Girsanov formula. 参考文献 | 相关文章 | 计量指标

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NONLINEAR EVOLUTION SYSTEMS AND GREEN'S FUNCTION 王维克 数学物理学报(英文版). 2010 (6):  2051-2063.  DOI: 10.1016/S0252-9602(10)60190-7 摘要 ( 781 )   RICH HTML PDF(202KB) ( 2475 )   收藏 In this paper, we will introduce how to apply Green's function method to get the pointwise estimates for the solutions of Cauchy problem of nonlinear evolution equations with dissipative  structure. First of all, we introduce the pointwise estimates of the time-asymptotic shape of the solutions of the isentropic Navier-Stokes equations and show to exhibit the generalized Huygen's principle. Then, for other nonlinear dissipative evolution equations, we will only introduce the result and give some brief explanations. Our approach is based on the detailed analysis of the Green's function of the linearized system and micro-local analysis, such as frequency decomposition and so on. 参考文献 | 相关文章 | 计量指标

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EFFECTIVE DYNAMICS OF A COUPLED MICROSCOPIC-MACROSCOPIC STOCHASTIC SYSTEM 任剑, 付红波, 曹道民, 段金桥 数学物理学报(英文版). 2010 (6):  2064-2076.  DOI: 10.1016/S0252-9602(10)60191-9 摘要 ( 755 )   RICH HTML PDF(187KB) ( 1098 )   收藏 A conceptual model for microscopic-macroscopic slow-fast stochastic systems is considered. A dynamical reduction procedure is presented in order to extract effective dynamics for this kind of systems. Under appropriate assumptions, the effective system is shown to approximate the original system, in the sense of a probabilistic convergence. 参考文献 | 相关文章 | 计量指标

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MULTIPLE STATIONARY SOLUTIONS OF EULER-POISSON EQUATIONS FOR NON-ISENTROPIC GASEOUS STARS 邓引斌, 谢华朝 数学物理学报(英文版). 2010 (6):  2077-2088.  DOI: 10.1016/S0252-9602(10)60192-0 摘要 ( 739 )   RICH HTML PDF(183KB) ( 1041 )   收藏 The motion of the self-gravitational gaseous stars can be described by the Euler-Poisson equations. The main purpose of this paper is concerned with the existence of stationary solutions of Euler-Poisson equations for some velocity fields and entropy functions that solve the conservation of mass and energy. Under different restriction to the strength of velocity field, we get the existence and multiplicity  of the stationary solutions of Euler-Poisson system. 参考文献 | 相关文章 | 计量指标

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ON A NEW 3D MODEL FOR INCOMPRESSIBLE EULER AND NAVIER-STOKES EQUATIONS 王术 数学物理学报(英文版). 2010 (6):  2089-2102.  DOI: 10.1016/S0252-9602(10)60193-2 摘要 ( 863 )   RICH HTML PDF(213KB) ( 1588 )   收藏 In this paper, we investigate some new properties of the incompressible Euler and Navier-Stokes equations by studying a 3D model for axisymmetric 3D incompressible Euler and Navier-Stokes equations with swirl. The 3D model is derived by reformulating the axisymmetric 3D incompressible Euler and Navier-Stokes equations and then neglecting the convection term of the resulting equations. Some properties of this 3D model are reviewed. Finally, some potential features of the incompressible Euler and Navier-Stokes equations such as the stabilizing effect of the convection are presented. 参考文献 | 相关文章 | 计量指标

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SMOOTHING ESTIMATES OF THE RADIAL SCHRÖDINGER PROPAGATOR IN DIMENSIONS n≥2 李栋, 张晓轶 数学物理学报(英文版). 2010 (6):  2103-2109.  DOI: 10.1016/S0252-9602(10)60194-4 摘要 ( 683 )   RICH HTML PDF(162KB) ( 1013 )   收藏 The usual Kato smoothing estimate for the Schr\"odinger propagator in 1D takes the form $\| |\partial_x|^{\frac 12} {\rm e}^{{\rm i}t\partial_{xx}} u_0 \|_{L_x^\infty L_t^2} \lesssim \| u_0 \|_{L_x^2}$. In dimensions $n\ge 2$ the smoothing estimate involves certain localization to cubes in space. In this paper we focus on radial functions and obtain Kato-type sharp smoothing estimates which can be viewed as natural eneralizations of the 1D Kato smoothing. These estimates are global in the sense that they do not need localization in space. We also present an interesting counterexample which shows that even though  the time-global inhomogeneous Kato smoothing holds true, the corresponding time-local inhomogeneous smoothing estimate cannot hold in general. 参考文献 | 相关文章 | 计量指标

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SPIRAL SOLUTION TO THE TWO-DIMENSIONAL TRANSPORT EQUATIONS 王振, 张庆玲 数学物理学报(英文版). 2010 (6):  2110-2128.  DOI: 10.1016/S0252-9602(10)60195-6 摘要 ( 1157 )   RICH HTML PDF(249KB) ( 1268 )   收藏 The existence of spiral solution for the two-dimensional transport equations is considered in the present paper. Based on  the notion of generalized solutions in the sense of Lebesgue-stieltjes integral, the global weak solution  of transport equations which includes δ-shocks and vacuum is constructed for some special initial data. 参考文献 | 相关文章 | 计量指标