Exact solutions of Diffusion Equation on sphere

Abstract

‎We examine the diffusion‎ ‎equation on the sphere‎. ‎In this sense‎, ‎we answer question of the symmetry classification‎. ‎We provide the algebra of symmetry and build‎ ‎the optimal system of Lie subalgebras‎. ‎We prove for one-dimensional optimal systems of Eq‎.(4), ‎space is expanding Ricci solitons‎. ‎Reductions of similarities related to subalgebras are classified‎, ‎and some exact invariant solutions of the diffusion‎ ‎equation on the sphere are presented‎.