Solutions entropiques de problèmes non linéaires dégénerés

Abstract

We consider a class of elliptic-hyperbolic degenerate equations g(u) - Delta b(u) + div phi(u) = f With Dirichlet homogeneous boundary conditions, and a class of elliptic-parabolic-hyperbolic degenerate equations g(u)(t) - Delta b(u) + div phi(u) = f with homogeneous Dirichlet conditions and initial conditions. The existence and uniqueness of entropy solutions for both problems are proved for nondecreasing continuous functions g and b vanishing at zero, and for continuous vectorial function satisfying rather general conditions.