Convergence of difference approximation of nonlinear evolution equations (Q1111343)

There has been a substantial development of the theory of nonlinear time- dependent evolution equations in Banach spaces. The results have been applied to a variety of problems of the approximation-solvability of nonlinear partial differential equations. This is a survey article which outlines recent work concerning the construction of mild solutions of such nonlinear evolution equations and various operator theoretic approaches to initial-boundary value problems for some typical nonlinear equations.