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

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 $b(x)$ 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.