On the isovectors of a class of nonlinear diffusion equations (Q580114)

A class of nonlinear diffusion equations is expressed in terms of an ideal of exterior differential forms. The components of the associated isovector field are constructed by using its transport property under Lie's derivative. The solution of the corresponding orbital equations generate an invariant group of transformations which reduce the nonlinear diffusion equation to an ordinary differential equation. For the problem of heat propagation, in an initially cool infinite media, due to a plane source, an exact solution is derived.