Homology and the Nonlinear Heat Diffusion Equation
J. R. Burgan, Alain Munier, Marc Roy Feix, Eric Fijalkow · SIAM Journal on Applied Mathematics · 1984
The concept of homology (SIAM J. Appl. Math., 40 (1981), pp. 191–207) is generalized to an arbitrary nonlinear diffusion equation. A large class of self-homologous diffusion coefficients is introduced and used to examine possible changes in initial and boundary conditions through homologous transformations. Generalized homology is shown to be identical to Bäcklund transformations.