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THE PHYSICAL ENTROPY OF SINGLE CONSERVATION LAWS

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Journal of Computational mathematics 1998年第5期16卷 437-444页

作者： (department of mathematics, Peking university, Beijing 100871, China) Beijing Univ Dept Math Beijing 100871 Peoples R China

By means of the comparisons with the formulas in statistical mechanics and thermodynamics, in this paper it is demonstrated that for the single conservation law partial derivative(t)u + partial derivative(x)f(u) = 0, if the flux function f(u) is convex (or concave), then, the physical entropy is S = -f(u); Furthermore, if we assume this result can be generalized to any f(u) with two order continuous derivative, from the thermodynamical principle that the local entropy production must be non-negative, one entropy inequality is derived, by which the O.A. Olejnik's famous E- condition can be explained successfully in physics.

关键词： conservation laws entropy entropy production

CMC surfaces in the hyperbolic 3-space

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Chinese Science Bulletin 1998年第7期43卷 547-550页

作者： YU Zuhuan 1, 2 and LI Zhenqi 1, 3 1. Institute of mathematics, Fudan university, Shanghai 200433, China 2. department of mathematics,Sichuan Union university, Chengdu 610064, China 3. department of mathematics, Nanchang university, Nanchang 33 nstitute of Mathemalics Fudan University Shanghai China department of mathematics Sichuan Union University Chengdu China department of mathematics Nanchang University Nanchang China

CMC-H surfaces satisfying H≥1 are studied. It is proved that these surfaces possess a natural representation which is a generalization of the Bryant’s result.

关键词： hyperbolic space CMC surface Weierstrass representation.

Smoothness for the collision local times of bifractional Brownian motions

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Science China mathematics 2011年第9期54卷 1859-1873页

作者： SHEN GuangJun 1,2,& YAN LiTan 3 1 department of mathematics,East China university of Science and Technology,Shanghai 200237,China 2 department of mathematics,Anhui Normal university,Wuhu 241000,China 3 department of mathematics,Donghua university,Shanghai 201620,China 1. department of mathematics East China University of Science and Technology Shanghai 200237 China2. Department of Mathematics Anhui Normal University Wuhu 241000 China3. Department of Mathematics Donghua University Shanghai 201620 China

Let B^Hi,Ki ={ Bt^Hi,Ki, t ≥ 0}, i= 1, 2 be two independent bifractional Brownian motions with respective indices Hi ∈ （0, 1） and K∈ E （0, 1]. One of the main motivations of this paper is to investigate f0^Tδ（Bs^H1 ,K1 - the smoothness of the collision local time, introduced by Jiang and Wang in 2009, IT = f0^T δ（Bs^H1,K1）ds, T 〉 0, where 6 denotes the Dirac delta function. By an elementary method, we show that iT is smooth in the sense of the Meyer-Watanabe if and only if min{H-1K1, H2K2} 〈-1/3.

关键词： bifractional Brownian motion collision local time intersection local time chaos expansion

ω-Gorenstein injective modules and dimensions

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Science China mathematics 2011年第3期54卷 421-436页

作者： ZHU HaiYan1,2 & DING NanQing3 1department of mathematics, Zhejiang university, Zhejiang 310027, China 2department of mathematics, Zhejiang university of Technology, Zhejiang 310023, China 3department of mathematics, Nanjing university, Nanjing 210093, China 1. department of mathematics Zhejiang University Zhejiang 310027 China2. Department of Mathematics Zhejiang University of Technology Zhejiang 310023 China3. Department of Mathematics Nanjing University Nanjing 210093 China

Gorenstein injective modules and dimensions have been studied extensively by many authors. In this paper, we investigate Gorenstein injective modules and dimensions relative to a Wakamatsu tilting module.

关键词： Wakamatsu tilting module ω-Gorenstein injective module ω-Gorenstein injective dimension cotilting module

Global existence of smooth solutions to two-dimensional compressible isentropic Euler equations for Chaplygin gases

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Science China mathematics 2010年第3期53卷 719-738页

作者： KONG DeXing 1 , LIU KeFeng 2 & WANG YuZhu 3, 1 department of mathematics, Zhejiang university, Hangzhou 310027, China 2 department of mathematics, university of California at Los Angeles, CA 90095, USA 3 department of mathematics, Shanghai Jiao Tong university, Shanghai 200248, China 1. department of mathematics Zhejiang University Hangzhou 310027 China2. Department of Mathematics University of California at Los Angeles Los Angeles CA 90095 USA3. Department of Mathematics Shanghai Jiao Tong University Shanghai 200248 China

In this paper we investigate the two-dimensional compressible isentropic Euler equations for Chaplygin gases. Under the assumption that the initial data is close to a constant state and the vorticity of the initial velocity vanishes, we prove the global existence of the smooth solution to the Cauchy problem for twodimensional flow of Chaplygin gases.

关键词： Chaplygin gases compressible Euler equations irrotational flow null condition Cauchy problem smooth solution

The maximal super-singular integral operators on product spaces

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Science China mathematics 2011年第12期54卷 2615-2626页

作者： WANG Hui1 & CHEN JieCheng2,3, 1department of mathematics, Xidian university, Xi’an 710071, China 2department of mathematics, Zhejiang Normal university, Jinhua 321004, China 3department of mathematics, Zhejiang university, Hangzhou 310027, China 1. department of mathematics Xidian University Xi’an 710071 China2. Department of Mathematics Zhejiang Normal University Jinhua 321004 China3. Department of Mathematics Zhejiang University Hangzhou 310027 China

We study the maximal super-singular integral operator T＊Ω,α,β（f）（x,y）=sup ∈1〉0,∈2〉0｜∫｜u｜〉ε1,｜v｜〉ε2 b1（｜u｜）b2（｜u｜）Ω（u＇,u＇）/｜u｜^n＋α｜u｜^m＋β-f（x-u,y-u）dudu｜defined on all f ∈ S（R^n ×R^m）, where 0 ≤ α,β〈∞, b1 b2 ∈ L∞（R＋1 ）,Ω satisfies certain cancellation conditions and Ω∈L1（S^n-1×S^m-1）in the case α,β〉0;Ω∈L（log＋L）（S^n-1×S^m-1）in the case αβ=0 and α＋β 〉0. It is proved that, for 1〈p〈∞.T＊Ω,α,βis a bounded operator from the homogeneous Sobolev space Lα,β^p（R^n×R^m）to the Lebesgue space L^p（R^n×R^m）.

关键词： super-singular integral maximal operator product spaces

Global existence and blow-up of solutions to a parabolic system with nonlocal sources and boundaries

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Science China mathematics 2007年第9期50卷 1251-1266页

作者： Ling-hua KONG~(1+) Ming-xin WANG~(2,3) 1 department of Applied mathematics,Dalian university of Technology,Dalian 116024,China 2 department of mathematics,Southeast university,Nanjing 210018,China 3 department of mathematics,Xuzhou Normal university,Xuzhou 221116,China department of Applied mathematics Dalian University of Technology Dalian 116024 China department of mathematics Southeast University Nanjing 210018 China department of mathematics Xuzhou Normal University Xuzhou 221116 China

This paper deals with a semi-linear parabolic system with nonlinear nonlocal sources and nonlocal boundaries. By using super-and sub-solution techniques, we first give the sufficient conditions that the classical solution exists globally and blows up in a finite time respectively, and then give the necessary and sufficient conditions that two components u and ν blow up simultaneously. Finally, the uniform blow-up profiles in the interior are presented.

关键词： parabolic system nonlocal sources nonlocal boundary conditions blow-up set simultaneous blow-up uniform blow-up profile 35K15 35K65

ON　CERTAIN　BOUNDARY　VALUE　PROBLEMS　FOR　NONLINEAR　INTEGRODIFFERENTIAL　EQUATIONS

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Acta Mathematica Scientia 1994年第2期14卷 226-234页

作者： D. G. Pachpatte(department of mathematics and Statisics Marathwada university Aurangabad 431004 (Maharashtra), india) MARATHWADA UNIV DEPT MATH & STATAURANGABAD 431004MAHARASHTRAINDIA

In this paper we seek sufficient conditions for the existence, uniqueness and continuous dependene on parameter of solutions of certain boundary value problems for nonlinear integrodifferential equations. The main tool employed in our analysis is based on converting the problems into equivalent Volterra integral equations by means of Green's function representation and the application of the Banach fixed point theorem.

关键词：澹

Parabolic equation of the m-Laplacian with nonlinear boundary condition

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Chinese Science Bulletin 1998年第11期43卷 905-908页

作者： WANG Shu+ 1, 2, WANG Mingxin 3, XIE Chunhong 1 1. department of mathematics, Nanjing university, Nanjing 210093, China 2. department of mathematics, Henan university, Kaifeng 475001, China 3. department of Applied mathematics, Southeast university, department of Mathernntics Nanjing University Nanjing China department of mathematics Henan University Kaifeng China department of Applied mathematics Southeast University Nanjing China

The existence and nonexistence of global positive weak solutions of parabolic equation of the m-Laplician with nonlinear boundary condition are dealt with. The necessary and sufficient conditions on the existence of a... 详细信息

关键词： nonlinear boundary condition parabolic equation of m-Laplacian global solution blow-up.