Existence for Nonlinear Evolution Equations and Application to Degenerate Parabolic Equation - Ning Su; Li Zhang (Journal of Applied Mathematics)
We consider an abstract Cauchy problem for a doubly nonlinear evolution equation of the form d/dt𝒜u+ℬu∋ft in V′, t∈0, T, where V is a real reflexive Banach space, 𝒜 and ℬ are maximal monotone operators (possibly multivalued) from V to its dual V′. In view of some practical applications, we assume that 𝒜 and ℬ are subdifferentials. By using the back difference approximation, existence is established, and our proof relies on the continuity of 𝒜 and the coerciveness of ℬ. As an application, we give the existence for a nonlinear degenerate parabolic equation.