We consider an abstract Cauchy problem for a doubly nonlinear evolution equation of the form in , , where is a real reflexive Banach space, and are maximal monotone operators (possibly multivalued) from to its dual . In view of some practical applications, we assume that and are subdifferentials. By using the back difference approximation, existence is established, and our proof relies on the continuity of and the coerciveness of . As an application, we give the existence for a nonlinear degenerate parabolic equation.
"Existence for Nonlinear Evolution Equations and Application to Degenerate Parabolic Equation." J. Appl. Math. 2014 1 - 8, 2014. https://doi.org/10.1155/2014/567241