## Abstract and Applied Analysis

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

#### 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.

#### Article information

Source
Abstr. Appl. Anal., Volume 2014, Special Issue (2013), Article ID 840573, 9 pages.

Dates
First available in Project Euclid: 2 October 2014

https://projecteuclid.org/euclid.aaa/1412279792

Digital Object Identifier
doi:10.1155/2014/840573

Mathematical Reviews number (MathSciNet)
MR3178896

Zentralblatt MATH identifier
07023178

#### Citation

Li, Dongfang; Tong, Chao; Wen, Jinming. Stability of Exact and Discrete Energy for Non-Fickian Reaction-Diffusion Equations with a Variable Delay. Abstr. Appl. Anal. 2014, Special Issue (2013), Article ID 840573, 9 pages. doi:10.1155/2014/840573. https://projecteuclid.org/euclid.aaa/1412279792

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