Homology and the nonlinear heat diffusion equation
Abstract
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 selfhomologous 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 selfsimilar transformations.
 Publication:

SIAM Journal of Applied Mathematics
 Pub Date:
 February 1984
 Bibcode:
 1984SJAM...44...11B
 Keywords:

 Diffusion Coefficient;
 Homology;
 Nonlinear Equations;
 Thermal Diffusion;
 Thermodynamics;
 Transformations (Mathematics);
 Boundary Conditions;
 Boundary Value Problems;
 Fluid Mechanics and Heat Transfer