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SOME RESULTS OF A NEHARI FAMILY

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Chinese Annals of mathematics,Series B 2005年第1期26卷 57-66页

作者： ZHUHUACHENG YANGZONGXIN CHENJIXIU instituteofmathematics LaboratoryofMathematicsforNonlinearSciencesFudanUniversityShanghai200433China instituteofmathematics，{2.ofmathematicsfornonlinearsciences，fudanuniversity Shanghai200433China

The authors study the Nehari family Nb and obtain some important properties for this family.

关键词： Schwarzian derivative Nehari family

SOME REMARKS ON THE NULL CONDITION FOR nonlinear ELASTODYNAMIC SYSTEM

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Chinese Annals of mathematics,Series B 2002年第3期23卷 311-316页

作者： XIN JIE institute of mathematics, {2. of mathematics for nonlinear sciences, Pudan university, shanghai 200433, china. institute of mathematics Laboratory of Mathematics for Nonlinear Sciences Fudan University Shanghai 200433 China

The author derives the same null condition as in [1] for the nonlinear elastodynamic system in a simpler way and proves the equivalence of the null conditions introduced in [1] and [7] respectively.

关键词： Null condition Stored energy function Elastodynamic system

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 {2. sciences,Ministry of Education,china shanghai Key laboratory for Contemporary Applied mathematics School of Mathematical sciences,fudan university,shanghai {12.,china. Key laboratory of mathematics for {2. sciences Ministry of Education China shanghai Key laboratory for Contemporary Applied {2. 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.169,2.03,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

BLOW UP OF SOLUTIONS TO THE CAUCHY PROBLEM FOR nonlinear WAVE EQUATIONS

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Chinese Annals of mathematics,Series B 2001年第3期22卷 275-280页

作者： ZHOU YI institute of mathematics,{2., shanghai 200433, china institute of mathematics Fudan University Shanghai 200433 China

The author proves blow up of solutions to the Cauchy problem of certain nonlinear equations and, also, estimates the time when the blow up occurs.

关键词： Cauchy problem nonlinear wave equation Blow up

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 {2. 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 {2. 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

ON A CONSTRUCTION OF INERTIALMANIFOLDS FOR A CLASS OF SECOND ORDER IN TIME EVOLUTION EQUATIONS

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Chinese Annals of mathematics,Series B 1999年第3期20卷 271-278页

作者： WANG ZONGXIN(institute of mathematics,{2., shanghai 200433, china.) institute of mathematics Fudan University Shanghai 200433 China

Inertial manifolds for a class of second order in time dissipative equations are *** author also proves an asymptotic completeness property for the inertial manifolds and characterizes the inertial manifolds as the set of trajectories whose growth is at most of order O(e-μt ) for some p > 0. As applications, a nonlinear wave equation and a problem of nonlinear oscillations of a shallow shell are considered.

关键词： Dynamical systems Inertial manifolds nonlinear evolution equations

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 2.5006,{2. laboratory of mathematics for nonlinear sciences, fudan university, shanghai 200433,{2. School of Mathematical sciences Suzhou University Suzhou China laboratory of mathematics for {2. 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.

ON INTERACTION OF SHOCK AND SOUND WAVE (Ⅰ)

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Chinese Annals of mathematics,Series B 1996年第4期17卷 35-42页

作者： CHEN SHUXING(institute of mathematics,{2. shanghai 200433, china.) 复旦大学数学系上海

This paper studies the ioteraction of shock and gradient wave (sound wave) of solutions to the system of inviscid isentropic gas dynamics as a model for the corresponding problems for nonlinear hyperbolic systems. The problem can be reduced to a boundary value problem in a wedged domain. By using the method of constructing asymptotic solutions and Newton’s iteration process it is proved that if a weak shock hits a gradient wave, then the grandient wave will split into two gradient waves, while the shock continuses propagating. In this paper the author reduces the problem to a standard form and constructs asymptotic solution of the problem. The existence of the genuine solution will be given in the following paper.

关键词： Shock wave Sound wave Nonliner hyperbolic system Asymptotic solution

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 {2.,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