Rothe’s method to parabolic integra-differential equations via abstract integra-differential equations

Abstract

In this paper an abstract integrodiffe-rential equation associated with a singlevalued m-accretive operator is considered in a Banach space whose dual is uniformly convex. The existence and uniqueness of strong solution is proved with the help of Rothe's method. The established results are then applied to assert the existence of unique strong solution of a class of parabolic initial boundary value problems with memory