Approximation of solutions to linear integro-differential parabolic equations in L^p-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.