ENTROPY SOLUTIONS FOR FIRST-ORDER QUASILINEAR EQUATIONS RELATED TO A BILATERAL OBSTACLE CONDITION IN A BOUNDED DOMAIN

作     者：L. LEVI G. VALLET 

作者机构：Université de Pau & CNRS Laboratoire de Mathématiques Appliquées ERS 2055 I. P. R. A. Avenue de l'Université 64000 PAU France 

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

年 卷 期：2001年第22卷第1期

页      面：93-114页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

主　　题：Obstacle problem Measure-valued solution Scalar conservation law 

摘      要：This paper is devoted to the existence and the uniqueness of the entropy solution for a general scalar conservation law associated with a forced bilateral obstacle condition in a bounded domain of Rp, p= 1. The method of penalization is used with a view to obtaining an existence result. However, the former only gives uniform L -estimates and so leads in fact to look for an Entropy Measure-Valued Solution, according to the specific properties of bounded sequences in L . The uniqueness of this EMVS is proved. Classically, it first ensures the existence of a bounded and measurable function U entropy solution and then the strong convergence in Lq of approximate solutions to U.