Entropy Solutions for Nonlinear Degenerate Problems

We consider a class of elliptic-hyperbolic degenerate equations g(u)-Db(u) +divgf(u) = fg(u)-Delta b(u) +divgphi (u) =f with Dirichlet homogeneous boundary conditions and a class of elliptic-parabolic-hyperbolic degenerate equations g(u)_t-Db(u) +divgf(u) = fg(u)_t-Delta b(u) +divgphi (u) =f with homogeneous Dirichlet conditions and initial conditions. Existence of entropy solutions for both problems is proved for nondecreasing continuous functions g and b vanishing at zero and for a continuous vectorial function J satisfying rather general conditions. Comparison and uniqueness of entropy solutions are proved for g and b continuous and nondecreasing and for J continuous.