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

Abstract

We carry out the Lie symmetry classification for a class of systems of nonlinear diffusion equations with power nonlinearities. The kernel of the maximal Lie invariance algebras of this system is found, i.e., we determine the Lie invariance algebra admitted by the system for arbitrary exponents and arbitrary values of the diffusion coefficients. Furthermore, all inequivalent extensions of the kernel of the maximal Lie invariance algebras of the corresponding diffusion systems are classified.