On uniqueness and existence of entropy solutions for a nonlinear parabolic problem with absorption.
Résumé
The aim of this paper is to study, for L1-data, the absorption problem of parabolic type : u_t −div a(u, Du) + β(x, u) \ni f with Dirichlet boundary conditions and initial conditions. Here a satisfies the classical Leray-Lions hypotheses and β(x, ·) is the subdifferential ∂j(x, ·), where j is a convex function such that j(·, 0) = 0. Existence and uniqueness of an entropy solution is established.