Renormalized solution for Stefan type problems: existence and uniqueness
Résumé
We consider a class of nonlinear degenerate problems of Stefan type: $$u_t- \Delta w -\nabla F(u,w)= g(\cdot,u), \ w\in \beta(u)$$ where β is a maximal monotone graph in $${\mathbb{R}^2,}$$ with homogenous Dirichlet conditions and initial conditions. Under rather general assumptions on F and g, we prove existence and uniqueness of renormalized solutions.