Nonlocal Parabolic Integro-differential Equations with Delays

Abstract

In this paper we consider a parabolic integro-differential equation with delay and a nonlocal boundary condition. We apply the method of semidiscretization in time, also known as the method of lines, to establish the existence and uniqueness of the considered problem. We also establish the continuous dependence of the solution on the initial data. Finally, an application of the established results is demonstrated