Journal of Nonlinear Mathematical Physics

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
https://doi.org/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/).

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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
18 - Supplement 1
Pages
107 - 121
Publication Date
2021/01
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
https://doi.org/10.1142/S1402925111001301How to use a DOI?
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
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  - https://doi.org/10.1142/S1402925111001301
ID  - Galaktionov2021
ER  -