Exact results for the nonlinear diffusion equations delta u/ delta t= delta / delta x(u-4/3delta u/ delta x) and delta u/ delta t- delta / delta x(u-2/3delta u/ delta x)
- 21 December 1991
- journal article
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 24 (24), 5721-5745
- https://doi.org/10.1088/0305-4470/24/24/009
Abstract
The author exploits local and non-local symmetries of the two equations of the title and of some related equations. Some new exact solutions are derived and some specific boundary value problems of physical significance are considered.Keywords
This publication has 12 references indexed in Scilit:
- Some non-local transformations between nonlinear diffusion equationsJournal of Physics A: General Physics, 1990
- Similarity solutions for nonlinear diffusion ? a new integration procedureJournal of Engineering Mathematics, 1989
- Extremely High Concentration Dopant Diffusion in SiliconIMA Journal of Applied Mathematics, 1988
- Temperature distribution in square-shaped semiconductor chipsPhysica Status Solidi (a), 1988
- New classes of symmetries for partial differential equationsJournal of Mathematical Physics, 1988
- Group Transformations and the Nonlinear Heat Diffusion EquationSIAM Journal on Applied Mathematics, 1981
- Large time behaviour of solutions of the porous medium equation in bounded domainsJournal of Differential Equations, 1981
- Stability of the separable solution for fast diffusionArchive for Rational Mechanics and Analysis, 1980
- Evolution of a stable profile for a class of nonlinear diffusion equations with fixed boundariesJournal of Mathematical Physics, 1977
- Exact solutions in nonlinear diffusionJournal of Engineering Mathematics, 1974