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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2018, Volume 300, Pages 7–18
DOI: https://doi.org/10.1134/S0371968518010016 (Mi tm3863) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Symmetries of fundamental solutions and their application in continuum mechanics

A. V. Aksenov

Faculty of Mechanics and Mathematics, Moscow State University, Moscow, 119991 Russia
Full-text PDF (186 kB) Citations (2)
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DOI: https://doi.org/10.1134/S0371968518010016
Abstract: An application of the symmetries of fundamental solutions in continuum mechanics is presented. It is shown that the Riemann function of a second-order linear hyperbolic equation in two independent variables is invariant with respect to the symmetries of fundamental solutions, and a method is proposed for constructing such a function. A fourth-order linear elliptic partial differential equation is considered that describes the displacements of a transversely isotropic linear elastic medium. The symmetries of this equation and the symmetries of the fundamental solutions are found. The symmetries of the fundamental solutions are used to construct an invariant fundamental solution in terms of elementary functions.
Received: October 16, 2017
English version:
Proceedings of the Steklov Institute of Mathematics, 2018, Volume 300, Pages 1–12
DOI: https://doi.org/10.1134/S0081543818010017
Bibliographic databases:
Document Type: Article
UDC: 517.9+533.6+539.3
Language: Russian
Citation: A. V. Aksenov, “Symmetries of fundamental solutions and their application in continuum mechanics”, Modern problems and methods in mechanics, Collected papers. On the occasion of the 110th anniversary of the birth of Academician Leonid Ivanovich Sedov, Trudy Mat. Inst. Steklova, 300, MAIK Nauka/Interperiodica, Moscow, 2018, 7–18; Proc. Steklov Inst. Math., 300 (2018), 1–12
Citation in format AMSBIB
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\paper Symmetries of fundamental solutions and their application in continuum mechanics
\inbook Modern problems and methods in mechanics
\bookinfo Collected papers. On the occasion of the 110th anniversary of the birth of Academician Leonid Ivanovich Sedov
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\vol 300
\pages 7--18
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
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  • https://doi.org/10.1134/S0371968518010016
  • https://www.mathnet.ru/eng/tm/v300/p7
    • This publication is cited in the following 2 articles:
    1. A. V. Aksenov, H. Orelma, “Lie symmetries of fundamental solutions to the Leutwiler–Weinstein equation”, Potential Anal, 59:2 (2023), 789  crossref  mathscinet
    2. A. V. Aksenov, Nonlinear Physical Science, Symmetries and Applications of Differential Equations, 2021, 269  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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    Full-text PDF :60
    References:48
    First page:15
     
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