Premium
Nonfickian effect in time and space for diffusion processes
Author(s) -
Ferreira José A.,
Pena Gonçalo
Publication year - 2015
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.21962
Subject(s) - diffusion , diffusion equation , partial differential equation , mathematics , differential equation , space (punctuation) , anomalous diffusion , first order partial differential equation , mathematical analysis , convection–diffusion equation , innovation diffusion , computer science , thermodynamics , physics , knowledge management , economy , economics , service (business) , operating system
Diffusion processes are usually simulated using the classical diffusion equation. In certain scenarios, such equation induces anomalous behavior and consequently several improvements were introduced in the literature to overcome them. One of the most popular was the replacement of the diffusion 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 article, we consider mathematical models for diffusion processes that take into account a memory effect in time and space. © 2015 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 1589–1602, 2015