Homology and the nonlinear heat diffusion equation

A theorem is presented which generalizes the concept of homology, introduced by Munier et al. (1981), to a large class of nonlinear diffusion coefficients. Possible changes in both initial and boundary conditions induced by self-homologous transformations are investigated. In order to be consistent with previously established definitions, generalized homology is expressed in terms of a Baecklund transformation, the only remaining process to overstep self-similar transformations.