On uniqueness and existence of entropy solutions for a nonlinear parabolic problem with absorption.

Boris Andreianov (1) , Karima Sbihi (1, 2) , Petra Wittbold (3)

1 LMB - Laboratoire de Mathématiques de Besançon (UMR 6623)
2 IRMA - Institut de Recherche Mathématique Avancée
3 TU - Technical University of Berlin / Technische Universität Berlin

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.

Mots clés: absorption problem; weak and entropy solution; capacity; L1-data; nonlinear semigroup theory; doubling of variables.; doubling of variables

Domaines: Equations aux dérivées partielles [math.AP]

Boris Andreianov, Karima Sbihi, Petra Wittbold. On uniqueness and existence of entropy solutions for a nonlinear parabolic problem with absorption.. Journal of Evolution Equations, 2008, 8 (3), pp.449--490. ⟨10.1007/s00028-008-0365-8⟩. ⟨hal-00475748⟩