Invariant solutions of nonlinear diffusion equations with maximal symmetry algebra

Victor Galaktionov, S R Svirshchevskii

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1 Citation (Scopus)

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.
Original languageEnglish
Pages (from-to)107-121
Number of pages15
JournalJournal of Nonlinear Mathematical Physics
Volume18
Issue numberSupplement 1
DOIs
Publication statusPublished - 2011
Event14th International Conference on Modern Group Analysis - Vidsel, Sweden
Duration: 25 May 20102 Jun 2010

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