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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 476829, 8 pages
http://dx.doi.org/10.1155/2014/476829
Research Article

Conservation Laws and Exact Solutions for a Reaction-Diffusion Equation with a Variable Coefficient

1Department of Applied Mathematics, Kunming University of Science and Technology, Kunming, Yunnan 650093, China
2Department of Mathematics, College of Science, China Three Gorges University, Yichang, Hubei 443002, China

Received 5 June 2014; Accepted 19 July 2014; Published 5 August 2014

Academic Editor: Linghai Zhang

Copyright © 2014 Zhijie Cao and Yiping Lin. 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

In this paper a variable-coefficient reaction-diffusion equation is studied. We classify the equation into three kinds by different restraints imposed on the variable coefficient in the process of solving the determining equations of Lie groups. Then, for each kind, the conservation laws corresponding to the symmetries obtained are considered. Finally, some exact solutions are constructed.