Existence for Nonlinear Evolution Equations and Application to Degenerate Parabolic Equation

Abstract EN

We consider an abstract Cauchy problem for a doubly nonlinear evolution equation of the form d/dt?u+ℬu∋ft in V′, t∈0, T, where V is a real reflexive Banach space, ? and ℬ are maximal monotone operators (possibly multivalued) from V to its dual V′.

In view of some practical applications, we assume that ? and ℬ are subdifferentials.

By using the back difference approximation, existence is established, and our proof relies on the continuity of ? and the coerciveness of ℬ.

As an application, we give the existence for a nonlinear degenerate parabolic equation.