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Sibirskii Zhurnal Industrial'noi Matematiki, 2012, Volume 15, Number 4, Pages 38–50 (Mi sjim750)  

This article is cited in 3 scientific papers (total in 3 papers)

Exact solutions to the equations of the dynamic asymmetric model of elasticity

N. F. Belmetsev, Yu. A. Chirkunov

Novosibirsk State Technical University, Novosibirsk, Russia
Full-text PDF (266 kB) Citations (3)
References:
Abstract: Using the group stratification of the equations of the dynamic asymmetric model of elasticity effectively used in the study of elastic materials made of polymers, we obtain a system that, after renaming the functions, becomes equivalent to these equations and contains fewer additional functions than the union of the resolving and automorphic systems of the accomplished group stratification. Among first-order systems equivalent to these equations it contains the least number of additional functions and is the only such system up to a nondegenerate linear transformation of the additional functions. We find its principal Lie transformation group, an optimal system of its subgroups, and their universal invariants. Some invariant and partially invariant exact solutions are found; their physical meaning is explained.
Keywords: asymmetric elasticity, group stratification, optimal system of subgroups, invariant solutions.
Received: 01.06.2012
English version:
Journal of Applied and Industrial Mathematics, 2013, Volume 7, Issue 1, Pages 41–53
DOI: https://doi.org/10.1134/S1990478913010055
Bibliographic databases:
Document Type: Article
UDC: 517.956.32+539.3+517.956+512.816
Language: Russian
Citation: N. F. Belmetsev, Yu. A. Chirkunov, “Exact solutions to the equations of the dynamic asymmetric model of elasticity”, Sib. Zh. Ind. Mat., 15:4 (2012), 38–50; J. Appl. Industr. Math., 7:1 (2013), 41–53
Citation in format AMSBIB
\Bibitem{BelChi12}
\by N.~F.~Belmetsev, Yu.~A.~Chirkunov
\paper Exact solutions to the equations of the dynamic asymmetric model of elasticity
\jour Sib. Zh. Ind. Mat.
\yr 2012
\vol 15
\issue 4
\pages 38--50
\mathnet{http://mi.mathnet.ru/sjim750}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3112357}
\transl
\jour J. Appl. Industr. Math.
\yr 2013
\vol 7
\issue 1
\pages 41--53
\crossref{https://doi.org/10.1134/S1990478913010055}
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  • https://www.mathnet.ru/eng/sjim/v15/i4/p38
  • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Сибирский журнал индустриальной математики
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    Full-text PDF :128
    References:59
    First page:1
     
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