An iteration procedure for a class of integro-differential of parabolic type

Abstract

This paper deals with a class of integrodifferential equations of parabolic type in which a function of the solution and its derivatives up to the second order with respect to the space variables is involved in a definite integral over the region. The problem can be applied to various models in physics and engineering. An iteration approach is used to establish the global solvability and stability for the problem. The technique is based on estimates of Green's function along with Gronwall's inequality.