Approximation of solutions to linear integro-differential parabolic equations in Lp-spaces

In this paper we show that, under suitable assumptions, the solutions to the approximating initial and boundary value problems (PE) (cf. introduction) converge in LP((O, T); L-s(Omega)), for suitable indexes P E [1, + infinity) and s is an element of [1, +infinity), to the solution to the limitproblem (P-0). The lasttwo Sections 4-5 are devoted to a similar approximation result, in a Banach-space framework, and involve a generalization of the kernels k, h and operator A. (c) 2006 Elsevier Inc. All rights reserved.