Similarity reductions for a nonlinear diffusion equation
Analysis of PDEs
2015-06-26 v1
Abstract
Similarity reductions and new exact solutions are obtained for a nonlinear diffusion equation. These are obtained by using the classical symmetry group and reducing the partial differential equation to various ordinary differential equations. For the equations so obtained, first integrals are deduced which consequently give rise to explicit solutions. Potential symmetries, which are realized as local symmetries of a related auxiliary system, are obtained. For some special nonlinearities new symmetry reductions and exact solutions are derived by using the nonclassical method.
Cite
@article{arxiv.math/9807192,
title = {Similarity reductions for a nonlinear diffusion equation},
author = {Maria Luz Gandarias and P. Venero and José Ramírez-Labrador},
journal= {arXiv preprint arXiv:math/9807192},
year = {2015}
}