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

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.