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Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2008, Volume 5, Pages 42–50 (Mi semr90)  

Research papers

On group-theoretical properties of equation of dynamics of microsrtuctures

N. V. Lyubashevskaya

Novosibirsk State University
References:
Abstract: We discuss group-theoretical properties of equation describing formation and evolution of defects in microstructures. Invariant solutions of equation are obtained by optimal system of subalgebras of Lie algebra permissible by considering equation. It is shown that optimal system consists of $3$ one-dimensional subalgebras, $13$ two-dimensional subalgebras, $7$ tree-dimensional subalgebras. Each representative of optimal system generates invariant solution of rang $3$, $2$ or $1$ with corresponding number of independent variables. All factor equations describing invariant solutions of considering equation are constructed.
Received January 9, 2008, published March 10, 2008
Bibliographic databases:
Document Type: Article
UDC: 517.9
MSC: 22E67, 35Q99
Language: Russian
Citation: N. V. Lyubashevskaya, “On group-theoretical properties of equation of dynamics of microsrtuctures”, Sib. Èlektron. Mat. Izv., 5 (2008), 42–50
Citation in format AMSBIB
\Bibitem{Lyu08}
\by N.~V.~Lyubashevskaya
\paper On group-theoretical properties of equation of dynamics of microsrtuctures
\jour Sib. \`Elektron. Mat. Izv.
\yr 2008
\vol 5
\pages 42--50
\mathnet{http://mi.mathnet.ru/semr90}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2586621}
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