Uniqueness for nonlinear degenerate problems

We prove existence and uniqueness results for weak solutions of nonlinear degenerate problems arising in various physical models. The main novelty in the article concerns the uniqueness, which employs a technique based in showing that weak solutions are also entropy solutions, for which uniqueness follows from a straightforward adaptation of known results. We treat equations with lower order terms that have a particular structure and show with a counterexample that for general lower order terms the uniqueness does not hold.