Nonclassical symmetry reductions for an inhomogeneous nonlinear diffusion equation

摘要

In this paper we consider a class of generalised diffusion equations which are of great interest in mathematical physics. For some of these equations model, fast diffusion nonclassical symmetries are derived. We find the connection between classes of nonclassical symmetries of the equation and of an associated system. These symmetries allow us to increase the number of solutions. Some of these solutions are unobtainable by classical symmetries and exhibit an interesting behaviour.