An abstract partial functional integrodifferential equations

Abstract

In this work, we investigate the existence and regularity of solutions for some partial functional integrodifferential equations with finite delay. The continuous dependence upen initial values and asymptotic stability are also studied. Firstly, we show the existence of the mild solutions. Secondly, we give sufficient conditions ensuring the existence of the strict solutions. The method used treats the equations in the domain of A with the graph norm employing results from linear semigroup theory. To illustrate our abstract result, we conclude this work with an application.