Existence and uniqueness of solutions for a class of doubly degenerate parabolic equations

In this paper, we study the Dirichlet problem for degenerate parabolic equations of the form ∂u∂t−div(a(x,t,u,∇u))−divϕ(u)=f−divg, where the main operator a(x,t,u,∇u)a(x,t,u,∇u) is allowed to degenerate with respect to the unknown u. Under suitable conditions on a and ϕ, we prove that there exists an unique solution u of this problem.