Parabolic integrodifferential equations with nonhomogeneous boundary conditions
Daniela Sforza · Differential and Integral Equations · 1989
We consider a parabolic partial integrodifferential Volterra equation with nonhomogeneous boundary conditions {and a similar problem with infinite delay, where A is the Laplace operator and k: [0, +oc[--+ R Under suitable assumptions on the kernel k, we state some results about the existence, uniqueness and regularity of the solutions of (*) and of the equation with infinite delay. Introduction.This paper deals with a class of parabolic partial integrodifferential Volterra equations with nonhomogeneous boundary conditions {and the similar problem with infinite delay {with regular boundary an, A is the Laplace operator and the Laplace transform of k: [0, +oo[--+ IR verifies suitable assumptions.Many authors have studied problems (0.1) and (0.2) when 'P = 0 using Laplace transform and other methods; see for instance [1]-[5], [8]-[10].