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 ) ) − div ϕ ( u ) = f − div g , where the main operator 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.