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Generalized Tricomi Problem for a Quasilinear Mixed Type Equation

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Chinese Annals of Mathematics,Series B 2009年第5期30卷 527-538页

作者： shuxing chen school of mathematical sciences Fudan University Shanghai 200433 China

In this paper,the Tricomi problem and the generalized Tricomi problem for a quasilinear mixed type equation are *** coefficients of the mixed type equation are discontinuous on the line,where the equation changes its *** existence of solution to these problems is *** method developed in this paper can be used to study more difficult problems for nonlinear mixed type equations arising in gas dynamics.

关键词：混合型方程拟线性广义气体动力学方程非线性混合型不连续

TRICOMI PROBLEM FOR A MIXED EQUATION OF SECOND ORDER WITH DISCONTINUOUS COEFFICIENTS

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Acta Mathematica Scientia 2009年第3期29卷 569-582页

作者：陈恕行 school of mathematical sciences Fudan UniversityShanghai 200433 China

This paper is devoted to the Tricomi problem for a mixed type equation of second order. The coeffcients are assumed to be discontinuous on the line where the type is changed. The unique existence of the solution to the problem is proved if the domain is small enough. Correspondingly, some estimates on the solution is also established.

关键词： mixed type equation Tricomi problem Riemann function

A NONLINEAR LAVRENTIEV-BITSADZE MIXED TYPE EQUATION

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Acta Mathematica Scientia 2011年第6期31卷 2378-2388页

作者：陈恕行 school of mathematical sciences Fudan University

In this paper the Tricomi problem for a nonlinear mixed type equation is studied. The coefficients of the mixed type equation are discontinuous on the line, where the equation changes its type. The existence of solution to this problem is proved. The method developed in this paper can be applied to study more difficult problems for nonlinear mixed type equations arising in gas dynamics.

关键词： nonlinear mixed type equation Tricomi problem Lavrentiev-Bitsadze equation partial hodograph transformation

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 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：震动交感声波气体动力学数学模型

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 horizon.

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:{□ u = (ut ) 3 , n = 2, t = 0 : u = 0, u t = εg(x), x ∈ R 2 , where □= 2t- sum from i=1 to n 2 xi is the wave operator, g(x) ≡ 0 is a smooth non-negative function on R 2 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：非线性波动方程寿命锐度立方非线性柯西问题古典解清晰度时间

On the Equi-nuclearity of Roe Algebras of Metric Spaces

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Chinese Annals of Mathematics,Series B 2010年第4期31卷 519-528页

作者： Xiaoman chen Benyin FU Qin WANG school of mathematical sciences Fudan University Shanghai 200433 China Department of Applied Mathematics Donghua University Shanghai 200051 China

The authors define the equi-nuclearity of uniform Roe algebras of a family of metric spaces. For a discrete metric space X with bounded geometry which is covered by a family of subspaces {Xi}∞i=1, if {Cu*(Xi)}∞i=1 are equi-nuclear and under some proper gluing conditions, it is proved that Cu*(X) is nuclear. Furthermore, it is claimed that in general, the coarse Roe algebra C*(X) is not nuclear.

关键词：度量空间代数相等离散几何核武器子空间家庭

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 200433,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边值问题气体休克初始状态自相似性顶点角象限欧拉

Exponential Synchronization of the Linearly Coupled Dynamical Networks with Delays

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Chinese Annals of Mathematics,Series B 2007年第6期28卷 737-746页

作者： Xiwei LIU Tianping chen Laboratory of Nonlinear Mathematics Science School of Mathematical Sciences Fudan University Shanghai 200433 China Corresponding author. Laboratory of Nonlinear Mathematics Science School of Mathematical Sciences Fudan University Shanghai 200433 China

在这篇论文，作者与推迟的联合调查一连串的线性地联合的相同动态系统的同步。在这里，联合矩阵能是不对称的；可约。保证的一些标准延期无关；延期依赖者全球同步分别地被导出。联合延期是否是，被看那不到积极阀值，然后，联合网络将... 详细信息

在这篇论文，作者与推迟的联合调查一连串的线性地联合的相同动态系统的同步。在这里，联合矩阵能是不对称的；可约。保证的一些标准延期无关；延期依赖者全球同步分别地被导出。联合延期是否是，被看那不到积极阀值，然后，联合网络将被同步。随联合延期的增加，在另一方面，网络的同步稳定性将被制止，甚至最后同步 de。

关键词：时延同步化指数稳定性本征向量