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Non-Global Existence of regular solution to Initial Value Problem of Relativistic Euler Equations in R^(N)

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Annals of Applied Mathematics 2024年第3期40卷 249-261页

作者： Xingli Li Jianli Liu Manwai Yuen Department of Mathematics Shanghai UniversityShanghai 200444China Newtouch Center for Mathematics of Shanghai University Shanghai UniversityShanghai 200444China Department of Mathematics and Information Technology The Education University of Hong KongHong KongChina

In fluid mechanics and astrophysics,relativistic Euler equations can be used to describe the effects of special relativity which are an extension of the classical Euler *** this paper,we will consider the initial value problem of relativistic Euler equations in an initial bounded region of R *** the initial velocity satisfies max→x 0∈∂Ω(0)N∑i=1 v_(i)^(2)(0,→x 0)regular solution for the N-dimensional relativistic Euler equations.

关键词： Non-global existence relativistic Euler equations regular solution initial value problem

regular solutionS FOR SCHRODINGER EQUATION ON UNBOUNDED DOMAINS

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Acta Mathematica Scientia 1998年第4期18卷 387-393页

作者：任艳霞吴荣 Nankai Univ Dept Math Tianjin 300071 Peoples R China

The authors study a class of solutions,namely, regular solutions of the Schrodinger equation (1/2 Delta + q)u = 0 on unbounded domains. They definite the regular solutions in terms of sample path properties of Brownian motion and then characterize them by analytic method. In Section 4, they discuss the regular solution to the stochastic Dirichlet problem for the equation (1/2 Delta + q)u = 0 having limit alpha at infinity.

关键词： Schrodinger equation regular solution stochastic Dirichlet problem

THE regular solutionS OF THE ISENTROPIC EULER EQUATIONS WITH DEGENERATE LINEAR DAMPING

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Chinese Annals of Mathematics,Series B 2005年第4期26卷 583-598页

作者： ZHU XUSHENG WANG WEIKE School of Basic Sciences East China Jiaotong University Nanchang 330013 China School of Mathematics and Statistics Wuhan University Wuhan 430072 China. Department of Mathematics Shanghai Jiao Tong University Shanghai 200030 China.

The regular solutions of the isentropic Euler equations with degenerate linear damping for a perfect gas are studied in this paper. And a critical degenerate linear damping coefficient is found, such that if the degenerate linear damping coefficient is larger than it and the gas lies in a compact domain initially, then the regular solution will blow up in finite time; if the degenerate linear damping coefficient is less than it, then under some hvpotheses on the initial data. the regular solution exists globally.

关键词： Compressible isentropic Euler equations Degenerate linear damping regular solution Blow-up Global existence

Kinetic Pattern Formation with Intermolecular Interactions:A Modified Brusselator Model

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Chinese Journal of Polymer Science 2021年第12期39卷 1673-1679页

作者： Rui-Qi Sun Jian-Feng Li Hong-Dong Zhang Yu-Liang Yang Department of Macromolecular Science State Key Laboratory of Macromolecular Engineering of PolymersFudan UniversityShanghai 200438China

In this work,we modify the traditi onal Brusselator model to in corporate the intermolecular interactions,based on which a systematic study is performed on the pattern formation mediated by chemical reaction and phase *** is found that if the chemical reaction dominates,the pattern formation will be inhibited by the phase separation while if the phase separation dominates,the chemical reaction will preve nt,un der certain conditi ons,the domain size from growing which results in dissipative patter ns other tha n macroscopic phase separations.

关键词： Brusselator model regular solution Phase separation

ON SPINODAL BOUNDARIES OF Al-Li ALLOYS

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Acta Metallurgica Sinica(English Letters) 1995年第1期8卷 41-46页

作者： Wei, Yinghui Wang, Xiaotian Xi'an Jiaotong Univ Xi'an China

The spinodal decomposition can occur in Al-Li alloys containing 5.8-14.2 at.% Li at room temperature. The modutated structure wavelength is approximately 3.1 nm for com mercial Al-LI alloys. The limit composition of t... 详细信息

关键词： Al-Li alloy spinodal decomposition regular solution

Mean-field stochastic linear quadratic optimal control problems: closed-loop solvability

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Probability, Uncertainty and Quantitative Risk 2016年第1期1卷 37-60页

作者： Xun Li Jingrui Sun Jiongmin Yong Department of Applied Mathematics The Hong Kong Polytechnic UniversityHong KongChina Department of Mathematics University of Central FloridaOrlandoFL 32816USA

An optimal control problem is studied for a linear mean-field stochastic differential equation with a quadratic cost *** coefficients and the weighting matrices in the cost functional are all assumed to be *** strategies are introduced,which require to be independent of initial states;and such a nature makes it very useful and convenient in *** this paper,the existence of an optimal closed-loop strategy for the system(also called the closedloop solvability of the problem)is characterized by the existence of a regular solution to the coupled two(generalized)Riccati equations,together with some constraints on the adapted solution to a linear backward stochastic differential equation and a linear terminal value problem of an ordinary differential equation.

关键词： Mean-field stochastic differential equation Linear quadratic optimal control Riccati equation regular solution Closed-loop solvability