Volume 18, Issue Supplement 1, September 2011, Pages 107 - 121
Invariant Solutions of Nonlinear Diffusion Equations with Maximal Symmetry Algebra
Authors
V. A. Galaktionov
Department of Mathematical Sciences, University of Bath, Bath, UK,masvg@bath.ac.uk
S. R. Svirshchevskii
Finance University Moscow, Russia,svr@spp.keldysh.ru
Received 15 October 2010, Accepted 3 November 2010, Available Online 7 January 2021.
- DOI
- 10.1142/S1402925111001301How to use a DOI?
- Keywords
- Partial differential equations; Lie symmetries; invariant solutions
- Abstract
Nonlinear n-dimensional second-order diffusion equations admitting maximal Lie algebras of point symmetries are considered. Examples of invariant solutions, as well as of solutions on invariant subspaces for some nonlinear operators, are constructed for arbitrary n. A complete description of all possible types of invariant solutions is given in the case n = 2 for the equation possessing an infinitely dimensional symmetry algebra. The results obtained are generalized for the hyperbolic and other fourth-order parabolic equations of thin film and nonlinear dispersion type.
- Copyright
- © 2011 The Authors. Published by Atlantis Press and Taylor & Francis
- Open Access
- This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).
Cite this article
TY - JOUR AU - V. A. Galaktionov AU - S. R. Svirshchevskii PY - 2021 DA - 2021/01/07 TI - Invariant Solutions of Nonlinear Diffusion Equations with Maximal Symmetry Algebra JO - Journal of Nonlinear Mathematical Physics SP - 107 EP - 121 VL - 18 IS - Supplement 1 SN - 1776-0852 UR - https://doi.org/10.1142/S1402925111001301 DO - 10.1142/S1402925111001301 ID - Galaktionov2021 ER -