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Global Existence of Classical Solutions for Some Oldroyd-B Model via the Incompressible Limit

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Chinese Annals of Mathematics,Series B 2006年第5期27卷 565-580页

作者： Zhen LEI school of mathematical sciences, fudan university, shanghai 200433, china.school of Mathematics and Statistics, Northeast Normal university, Changchun 130024, china. school of mathematical sciences Fudan University Shanghai 200433 China school of Mathematics and Statistics Northeast Normal University Changchun 130024 China

In this paper, we prove local and global existence of classical solutions for a system of equations concerning an incompressible viscoelastic fluid of Oldroyd-B type via the incompressible limit when the initial data ... 详细信息

关键词： Incompressible limit Global existence Oldroyd model

The fundamental solution of the Keldysh typeoperator

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Science china.Mathematics 2009年第9期52卷 1829-1843页

作者： CHEN ShuXing school of mathematical sciences, fudan university, shanghai 200433, china school of mathematical sciences Fudan University Shanghai China

In this paper we discuss the fundamental solution of the Keldysh type operator $ L_\alpha u \triangleq \frac{{\partial ^2 u}} {{\partial x^2 }} + y\frac{{\partial ^2 u}} {{\partial y^2 }} + \alpha \frac{{\partial u}} {{\partial y}} $ , which is a basic mixed type operator different from the Tricomi operator. The fundamental solution of the Keldysh type operator with $ \alpha > - \fracge ge $ is obtained. It is shown that the fundamental solution for such an operator generally has stronger singularity than that for the Tricomi operator. Particularly, the fundamental solution of the Keldysh type operator with $ \alpha ge ge $ has to be defined by using the finite part of divergent integrals in the theory of distributions.

关键词： mixed type equation Keldysh operator fundamental solution finite part of divergent integral 35M10 35A08

Global Classical Solutions to Partially Dissipative Quasilinear Hyperbolic Systems

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Chinese Annals of Mathematics,Series B 2011年第5期32卷 771-780页

作者： Yi ZHOU 11 Key Laboratory of Mathematics for Nonlinear sciences,Ministry of Education,china.shanghai Key Laboratory for Contemporary Applied Mathematics school of mathematical sciences,fudan university,shanghai 200433,china. Key Laboratory of Mathematics for Nonlinear sciences Ministry of Education China shanghai Key Laboratory for Contemporary Applied Mathematics school of mathematical sciences Fudan University Shanghai China

The author considers the Cauchy problem for quasilinear inhomogeneous hyperbolic *** the assumption that the system is weakly dissipative,Hanouzet and Natalini established the global existence of smooth solutions for small initial data (in *** ***.,Vol.169,2003,pp.89-117).The aim of this paper is to give a completely different proof of this result with slightly different assumptions.

关键词： Cauchy problem Global classical solution Partially dissipativequasilinear hyperbolic system

Sharpness on the Lower Bound of the Lifespan of Solutions to Nonlinear Wave Equations

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Chinese Annals of Mathematics,Series B 2011年第4期32卷 521-526页

作者： Yi ZHOU 1 Wei HAN 2 1 Nonlinear mathematical Modeling and Methods Laboratory shanghai Key Laboratory for Contem- porary Applied Mathematics school of mathematical sciences, fudan university, shanghai 200433, china. 2 school of mathematical sciences, fudan university, shanghai 200433, china.Department of Mathematics, North university of china. Taiyuan 030051, china. Nonlinear mathematical Modeling and Methods Laboratory shanghai Key Laboratory for Contemporary Applied Mathematics school of mathematical sciences Fudan University Shanghai China school of mathematical sciences Fudan University Shanghai China Department of Mathematics North University of China Taiyuan China

This paper is devoted to proving the sharpness on the lower bound of the lifespan of classical solutions to general nonlinear wave equations with small initial data in the case n = 2 and cubic nonlinearity （see the results of T. T. Li and Y. M. Chen in 1992）. For this purpose, the authors consider the following Cauchy problem： { where □=δt^2-∑i=1n δx^^2 is the wave operator, g（x）（≡/） 0 is a smooth non-negative function with compact support, and ε 〉 0 is a small parameter. It is shown that the solution blows up in a finite time, and the lifespan T（ε） of solutions has an upper bound T（ε） ≤ exp（Aε-2） with a positive constant A independent of ε, which belongs to the same kind of the lower bound of the lifespan.

关键词： Nonlinear wave equation Cauchy problem Lifespan

Blow Up of Solutions to Semilinear Wave Equations with Critical Exponent in High Dimensions

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Chinese Annals of Mathematics,Series B 2007年第2期28卷 205-212页

作者： Yi ZHOU school of mathematical sciences Fudan University Shanghai 200433 China

In this paper, the author considers equations with critical exponent in n ≥4 space tions on the initial data, it is proved that there small the initial data are. the Cauchy problem for semilinear wave dimensions. Und... 详细信息

关键词： Semilinear wave equation Critical exponent Cauchy problem Blow up

RADIAL BASIS FUNCTION INTERPOLATION IN SOBOLEV SPACES AND ITS APPLICATIONS

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Journal of Computational Mathematics 2007年第2期25卷 201-210页

作者： Manping Zhang (school of mathematical sciences,fudan university,shanghai 200433,china.Institute of Computational Mathematics,Chinese Academy of sciences,Beijing 100080,china school of mathematical sciences fudan university Shanghai 200433

In this paper we study the method of interpolation by radial basis functions and give some error estimates in Sobolev space H^k（Ω）（k 〉 1）. With a special kind of radial basis function, we construct a basis in H^k（Ω） and derive a meshless method for solving elliptic partial differential equations. We also propose a method for computing the global data density.

关键词： Sobolev space Radial basis function Global data density Meshless method

Hyperbolic positive mass theorem under modified energy condition

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Science china.Mathematics 2008年第12期51卷 2189-2197页

作者： XIE NaQing Institute of Mathematics, school of mathematical sciences, fudan university, shanghai 200433, china Institute of Mathematics School of Mathematical Sciences Fudan University Shanghai China

We provide two new positive mass theorems under respective modified energy conditions allowing T00 negative on some compact set for certain modified asymptotically hyperbolic manifolds. This work is analogous to Zhang... 详细信息

关键词： positive mass theorem modified energy condition modified asymptotically hyperbolic 83C40 53C27

SOBOLEV INEQUALITY ON RIEMANNIAN MANIFOLDS

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Chinese Annals of Mathematics,Series B 2005年第4期26卷 651-658页

作者： WANG MENG Department of Mathematics, Zhejiang university, Hangzhou 310027, china.school of mathematical sciences, Pudan university, shanghai 200433, china. Department of Mathematics Zhejiang University Hangzhou 310027 China school of mathematical sciences Fudan University Shanghai 200433 China

Let M be an n dimensional complete Riemannian manifold satisfying the doublingvolume property and an on-diagonal heat kernel estimate. The necessary-sufficientcondition for the Sobolev inequality ‖f‖q ≤ Cn,,v,p,q(... 详细信息

关键词： Sobolev inequality Complete manifold Riesz transform Potential Heat kernel

Jensen's Inequality for Backward Stochastic Differential Equations

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Chinese Annals of Mathematics,Series B 2006年第5期27卷 553-564页

作者： Long JIANG Department of Mathematics, china.university of Mining and Technology, Xuzhou 221008, Jiangsu, china.school of mathematical sciences, fudan university, shanghai 200433, china.school of Mathematics and System sciences, Shandong university, Jinan 250100, china. Department of Mathematics China University of Mining and Technology Xuzhou 221008 Jiangsu China school of mathematical sciences Fudan University Shanghai 200433 China school of Mathematics and System sciences Shandong University Jinan 250100 China

Under the Lipschitz assumption and square integrable assumption on g, the author proves that Jensen＇s inequality holds for backward stochastic differential equations with generator g if and only if g is independent of y, g（t, 0）≡ 0 and g is super homogeneous with respect to z. This result generalizes the known results on Jensen＇s inequality for gexpectation in [4, 7-9].

关键词： Backward stochastic differential equation g-Expectation Jensen's inequality for g-expectation Jensen's inequality for BSDEs