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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 > - \frac{1} {2} $ 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 < \frac{1} {2} $ 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

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

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

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

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

THE DISTANCE BETWEEN DIFFERENT COMPONENTS OF THE UNIVERSAL TEICHMULLER SPACE

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Chinese Annals of Mathematics,Series B 2005年第4期26卷 537-542页

作者： WANG ZHE school of mathematical sciences Fudan University Shanghai 200433 China.

The model of the universal Teichmuller union of infinite disconnected components. between different components is 0, and the every other component is 2. space by the derivatives of logarithm is the In this paper, it i... 详细信息

关键词： Universal Teichmuller space Logarithmic derivative Quasiconformal extension

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

Invariant tori for asymptotically linear impact oscillators

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Science china Mathematics 2006年第5期49卷 669-687页

作者： QIAN Dingbian & SUN Xiying school of mathematical sciences, Suzhou university, Suzhou 215006, china Laboratory of Mathematics for Nonlinear sciences, fudan university, shanghai 200433, china school of mathematical sciences Suzhou University Suzhou China Laboratory of Mathematics for Nonlinear sciences Fudan University Shanghai China

The existence of invariant tori and quasi-periodic solutions for asymptotically linear impact oscillators is proved by using the successor map and some generalized versions of the Moser's twist theorem.

关键词： invariant tori, boundedness of solutions, quasi-periodic solution, impact oscillator.

Approximate solutions to infinite dimensional LQ problems over infinite time horizon

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Science china Mathematics 2006年第7期49卷 865-876页

作者： PAN Liping, ZHANG Xu & CHEN Qihong school of mathematical sciences, fudan university, shanghai 200433, china school of Mathematics, Sichuan university, Chengdu 610064, china Department of Applied Mathematics, shanghai university of Finance & Economics, shanghai 200433, china school of mathematical sciences Fudan University Shanghai China school of Mathematics Sichuan University Chengdu China Department of Applied Mathematics Shanghai University of Finance & Economics Shanghai China

This paper is addressed to develop an approximate method to solve a class of infinite dimensional LQ optimal regulator problems over infinite time horizon. Our algorithm is based on a construction of approximate solutions which solve some finite dimensional LQ optimal regulator problems over finite time horizon, and it is shown that these approximate solutions converge strongly to the desired solution in the double limit sense.

关键词： approximate solution LQ problem infinite dimensional infinite time hori-