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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 840573, 9 pages
http://dx.doi.org/10.1155/2014/840573
Research Article

Stability of Exact and Discrete Energy for Non-Fickian Reaction-Diffusion Equations with a Variable Delay

1School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, China
2School of Computer Science and Engineering, Beihang University, Beijing 100191, China
3School of Computer Science, McGill University, Montreal, QC, Canada H3A 2K6
4Department of Mathematics and Statistics, McGill University, Montreal, QC, Canada H3A 2K6

Received 4 December 2013; Revised 28 December 2013; Accepted 11 January 2014; Published 5 March 2014

Academic Editor: Adem Kilicman

Copyright © 2014 Dongfang Li et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

This paper is concerned with the stability of non-Fickian reaction-diffusion equations with a variable delay. It is shown that the perturbation of the energy function of the continuous problems decays exponentially, which provides a more accurate and convenient way to express the rate of decay of energy. Then, we prove that the proposed numerical methods are sufficient to preserve energy stability of the continuous problems. We end the paper with some numerical experiments on a biological model to confirm the theoretical results.