Existence for nonlinear evolution equations and application to degenerate parabolic equation (Q2336542)

Summary: We consider an abstract Cauchy problem for a doubly nonlinear evolution equation of the form \((d/d t) \mathcal{A} (u) + \mathcal{B} (u) \ni f (t)\) in \(V', t \in (0, T]\), where \(V\) is a real reflexive Banach space, \(\mathcal{A}\) and \(\mathcal{B}\) are maximal monotone operators (possibly multivalued) from \(V\) to its dual \(V'\). In view of some practical applications, we assume that \(\mathcal{A}\) and \(\mathcal{B}\) are subdifferentials. By using the back difference approximation, existence is established, and our proof relies on the continuity of \(\mathcal{A}\) and the coerciveness of \(\mathcal{B}\). As an application, we give the existence for a nonlinear degenerate parabolic equation.