Application of Lie point symmetries to the resolution of an interface problem in a generalized Fisher equation

Abstract

In this work, we study a generalized reaction–diffusion Fisher equation using equivalence transfor- mations and Lie symmetries. Reaction–diffusion equations have been widely used for modeling the growth of tumors, brain gliomas in particular, and for modeling biological invasions. More recently, these models have been used to depict and explain various nonlinear physical, chemical, and biological phenomena. Finding analytical solutions describing the pass through white and gray matter in brain can be useful to describe the dynamics of glioma. Thus, we find analytical solutions for a model of tumor growth at its interface.