Symmetry analysis of a class of systems of nonlinear diffusion equations with power nonlinearities

Abstract

Lie symmetry classification has been performed for a class of systems of nonlinear diffusion equations with power-law nonlinearities. The kernel of symmetry algebras for the system under consideration was identified; specifically, the invariance algebra was established for the case of arbitrary exponents and arbitrary diffusion coefficients. Furthermore, all non-equivalent cases of parameter values that lead to an extension of the kernel of maximal Lie invariance algebras for the corresponding diffusion systems were determined.