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Symmetries and Fundamental Solutions of Displacement Equations for a Transversely Isotropic Elastic Medium

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Modern Mathematics and Mechanics

Part of the book series: Understanding Complex Systems ((UCS))

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Abstract

A fourth-order linear elliptic partial differential equation describing the displacements of a transversely isotropic linear elastic medium is considered. Its symmetries and the symmetries of an inhomogeneous equation with a delta function on the right-hand side are found. The latter symmetries are used to construct an invariant fundamental solution of the original equation in terms of elementary functions.

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Author information

Authors and Affiliations

  1. Lomonosov Moscow State University, Moscow, Russian Federation

    Alexander V. Aksenov

Authors
  1. Alexander V. Aksenov
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Editors and Affiliations

  1. Lomonosov Moscow State University, Moscow, Russia

    Victor A. Sadovnichiy

  2. National Technical University of Ukraine, “Igor Sikorsky Kyiv Polytechnic Institute”, Kyiv, Ukraine

    Michael Z. Zgurovsky

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Aksenov, A.V. (2019). Symmetries and Fundamental Solutions of Displacement Equations for a Transversely Isotropic Elastic Medium. In: Sadovnichiy, V., Zgurovsky, M. (eds) Modern Mathematics and Mechanics. Understanding Complex Systems. Springer, Cham. https://doi.org/10.1007/978-3-319-96755-4_8

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  • DOI: https://doi.org/10.1007/978-3-319-96755-4_8

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-96754-7

  • Online ISBN: 978-3-319-96755-4

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