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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 2.0433, china school of Mathematics, Sichuan university, chengdu 610064, china Department of Applied Mathematics, shanghai university of Finance & Economics, shanghai 2.0433, 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-

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, fudan university shanghai 2.0433, 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

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 2.0433, china. 2 school of mathematical sciences, fudan university, shanghai 2.0433, 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

Riemann boundary value problems and reflection of shock for the Chaplygin gas

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Science china Mathematics 2012年第4期55卷 671-685页

作者： chen shuxing 1,& QU AiFang 2 1 school of mathematical sciences,fudan university,shanghai 2.0433,china 2 Wuhan Institute of Physics and Mathematics,Chinese Academy of sciences,Wuhan 430071,china school of mathematical sciences Fudan University Shanghai China Wuhan Institute of Physics and Mathematics Chinese Academy of Sciences Wuhan China

In this paper,we study two-dimensional Riemann boundary value problems of Euler system for the isentropic and irrotational Chaplygin gas with initial data being two constant states given in two sectors respectively,where one sector is a quadrant and the other one has an acute vertex *** prove that the Riemann boundary value problem admits a global self-similar solution,if either the initial states are close,or the smaller sector is also near a *** result can be applied to solving the problem of shock reflection by a ramp.

关键词： Riemann boundary value problem reflection of shock Chaplygin gas wave interaction Eulersystem

Determination of Unknown Boundary in the Composite Materials with Stefan-Boltzmann Conditions

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Chinese Annals of Mathematics,Series B 2010年第2期31卷 145-162页

作者： Xiaoyi HU Wenbin chen school of mathematical sciences Fudan University Shanghai 200433 China.

Abstract The authors consider one specific kind of heat transfer problems in a threedimensional layered domain, with nonlinear Stefan-Boltzmann conditions on the boundaries as well as on the interfaces. To determine the unknown part of the boundary （or corrosion） by the Cauchy data on the reachable part is an important inverse problem in engineering. The mathematical model of this problem is introduced, the well-posedness of the forward problems and the uniqueness of the inverse problems are obtained.

关键词： Inverse heat problem Stefan-Boltzmann conditions Uniqueness

A New Approach to Synchronization Analysis of Linearly Coupled Map Lattices

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Chinese Annals of Mathematics,Series B 2007年第2期28卷 149-160页

作者： Wenlian LU Tianping chent Published online March school of mathematical sciences and Laboratory of Mathematics for Nonlinear sciences Fudan University Shanghai 200433 China.

In this paper, a new approach to analyze synchronization of linearly coupled map lattices （LCMLs） is presented. A reference vector x（t） is introduced as the projection of the trajectory of the coupled system on the synchronization manifold. The stability analysis of the synchronization manifold can be regarded as investigating the difference between the trajectory and the projection. By this method, some criteria are given for both local and global synchronization. These criteria indicate that the left and right eigenvectors corresponding to the eigenvalue ＂0＂ of the coupling matrix play key roles in the stability of synchronization manifold for the coupled system. Moreover, it is revealed that the stability of synchronization manifold for the coupled system is different from the stability for dynamical system in usual sense. That is, the solution of the coupled system does not converge to a certain knowable s（t） satisfying s（tT1） = f（s（t）） but to the reference vector on the synchronization manifold, which in fact is a certain weighted average of each x^i（t） for i=1,……, m, but not a solution s（t） satisfying s（t ＋ 1）=f（s（t））.

关键词： Linearly coupled map lattices Synchronization Synchronizationmanifold Local stability of synchronization manifold Global stability of synchronization manifold

Weierstrass Representation for Surfaces in the Three-Dimensional Heisenberg Group

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Chinese Annals of Mathematics,Series B 2010年第1期31卷 119-132页

作者： Qun chen Hongbing QIU school of Mathematics and Statistics Wuhan University Wuhan 430072 China Corresponding author. school of mathematical sciences Fudan University Shanghai 200433 China

The authors define the Gauss map of surfaces in the three-dimensional Heisenberg group and give a representation formula for surfaces of prescribed mean ***,a second order partial differential equation for the Gauss m... 详细信息

关键词： Heisenberg group Mean curvature Weierstrass representation

Induction of Epstein-Barr Virus Lytic Replication by Recombinant Adenoviruses Expressing the Zebra Gene with EBV Specific Promoters

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Acta Biochimica et Biophysica Sinica 2005年第4期37卷 215-220页

作者： Lu chen Juan YIN Yi chen Jiang ZHONG Department of Microbiology and Microbial Engineering,school of Life sciences,fudan university,shanghai 2.0433,china Department of Microbiology and Microbial Engineering School of Life Sciences Fudan University Shanghai 200433 China

The latent Epstein-Barr virus (EBV) is found in the cells of many *** example,EBVis detectable in almost all cases,and in almost all tumor cells,of non-keratinizing nasopharyngeal *** the latent virus,which will result in its lytic replication and the death of tumor cells,is a potentialapproach for the treatment of EBV-associated *** this study,three recombinant adenoviruses wereconstructed to express the Zebra gene,an EBV gene responsible for switching from the latent state to ***-specific promoters were used in order to limit Zebra expression in EBV-positive cells,andreduce the potential side *** EBV promoters used were Cp,Zp and a dual promoter combining *** Zebra protein was detected in HEK293 cells as well as the EBV-positive D98-HR1cells infected with recombinant *** EBV lyric replication early antigen,EA-D,was also detected ininfected D98-HR1,implying the initiation of lytic *** the cell viability assay,Zebra-expressingadenoviruses had little effect on EBV-negative HeLa cells,while significantly reducing the cell viability andproliferation of D98-HR1 *** results indicate that EBV virus promoters can be used in adenovirusvectors to express the Zebra gene and induce EBV lytic replication in D98-HR1 cells.

关键词： Epstein-Barr virus recombinant adenovirus lytic replication cancer

On the inner radius of univalency by pre-Schwarzian derivative

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Science china Mathematics 2007年第7期50卷 987-996页

作者： Tao chenG~(1,2+) Ji-xiu chen~1 1 school of mathematical sciences,fudan university,shanghai 2.0433,china 2 Department of Mathematics,Jiangxi Normal university,Nanchang 330022,china school of mathematical sciences Fudan University Shanghai China Department of Mathematics Jiangxi Normal University Nanchang China

In this paper,the inner radius of univalency of hyperbolic domains by pre-Schwarzian derivative is studied,and some general formulas for the lower bound of the inner radius are established. As their applications,the l... 详细信息

关键词： pre-Schwarzian derivative inner radius of univalency universal Teichmuller space 30C62 30F60