Generalized Persistence of Entropy Weak Solutions for System of Hyperbolic Conservation Laws

作     者：Yi ZHOU Yi ZHOU

作者机构：School of Mathematical SciencesFudan UniversityShanghai 200433China 

出 版 物：《Chinese Annals of Mathematics,Series B》 (数学年刊（B辑英文版）)

年 卷 期：2022年第43卷第4期

页      面：499-508页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：supported by the National Natural Science Foundation of China(No.12171097) Key Laboratory of Mathematics for Nonlinear Sciences(Fudan University),Ministry of Education of China,Shanghai Key Laboratory for Contemporary Applied Mathematics,School of Mathematical Sciences,Fudan University and Shanghai Science and Technology Program(No.21JC1400600) 

主　　题：Quasilinear hyperbolic system Cauchy problem Entropy weak solution Vanishing viscosity method 

摘      要：Let u(t,x)be the solution to the Cauchy problem of a scalar conservation law in one space *** is well known that even for smooth initial data the solution can become discontinuous in finite time and global entropy weak solution can best lie in the space of bounded total *** is impossible that the solutions belong to,for example,H^(1) because by Sobolev embedding theorem H^(1) functions are Holder ***,the author notes that from any point(t,x),he can draw a generalized characteristic downward which meets the initial axis at y=α(t,x).If he regards u as a function of(t,y),it indeed belongs to H^(1) as a function of y if the initial data belongs to H^(1).He may call this generalized persistence(of high regularity)of the entropy weak *** main purpose of this paper is to prove some kinds of generalized persistence(of high regularity)for the scalar and 2×2 Temple system of hyperbolic conservation laws in one space dimension.