Memory effect in time and space in non Fickian diffusion phenomena

Abstract

Usually diffusion processes are simulated using the classical diffusion equation. In certain scenarios such equation induces anomalous behaviour and consequently several improvements were introduced in the literature to overcome them. One of the most popular was the replacement of the di↵usion equation by an integro-differential equation. Such equation can be established considering a modification of Fick’s mass flux where a delay in time is introduced. In this paper we consider mathematical models for diffusion processes that take into account a memory effect in time and space.