Regularity of Fluxes in Nonlinear Hyperbolic Balance Laws

作     者：Matania Ben-Artzi Jiequan Li Matania Ben-Artzi;Jiequan Li

作者机构：Institute of MathematicsHebrew University of Jerusalem91904 JerusalemIsrael Academy of Multidisciplinary StudiesCapital Normal UniversityBeijing 100048China State Key Laboratory for Turbulence Research and Complex SystemPeking UniversityBeijing 100871China 

出 版 物：《Communications on Applied Mathematics and Computation》 (应用数学与计算数学学报（英文）)

年 卷 期：2023年第5卷第3期

页      面：1289-1298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：the Institute of Applied Physics and Computational Mathematics,Beijing,for the hospitality and support.The second author is supported by the NSFC(Nos.11771054,12072042,91852207) the Sino-German Research Group Project(No.GZ1465) the National Key Project GJXM92579 

主　　题：Balance laws Hyperbolic conservation laws Multi-dimensional Discontinuous solutions Finite-volume schemes Flux Trace on boundary 

摘      要：This paper addresses the issue of the formulation of weak solutions to systems of nonlinear hyperbolic conservation laws as integral balance *** basic idea is that the“meaningful objectsare the fluxes,evaluated across domain boundaries over time *** fundamental result in this treatment is the regularity of the flux trace in the multi-dimensional *** implies that a weak solution indeed satisfies the balance *** fact,it is shown that the flux is Lipschitz continuous with respect to suitable perturbations of the *** should be emphasized that the weak solutions considered here need not be entropy ***,the assumption imposed on the flux f(u)is quite minimal-just that it is locally bounded.