Symmetry groups and fundamental solutions for systems of parabolic equations

Abstract

In this paper, the relationship between Lie point symmetry and fundamental solution for systems of parabolic equations is explored. It is shown that the fundamental solutions of the systems of parabolic equations admitting certain symmetries can be obtained by inverting the Laplace transformation of the corresponding group-invariant solutions. Several examples are presented to illustrate the approach. Furthermore, the relationship between fundamental solutions for two systems of parabolic equations related by an equivalence transformation is identified.