On symmetries of radially symmetric nonlinear diffusion equation

Abstract

In this paper symmetries are sought for radially symmetric nonlinear diffusion equations of the type ut=r1-N[r N-1f(u)ur]r. The nonlinear forms of this equation which admit Lie classical symmetries are completely classified and are shown to exist when f=un, eu. Also, a trivial symmetry exists for arbitrary f. Lie-Bäcklund symmetries are also considered when f=un and shown to exist when n=0 (linear case) and when n= -2 and N= 1. © 1992 American Institute of Physics.