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 (Pε) (cf. introduction) converge in Lp((0,T );Ls(Ω)), for suitable indexes p ∈ [1,+∞) and s ∈ [1,+∞), to the solution to the limit problem (P0). The last two 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. © 2006 Elsevier Inc. All rights reserved.