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Fundamental solution of the elasticity theory equations in displacements for a transversely isotropic medium

Fundamental solution of the elasticity theory equations in displacements for a transversely... We consider a linear fourth-order elliptic partial differential equation describing the displacements of a transversely isotropic linearly elastic medium. We find the symmetries of this equation and of the inhomogeneous equation with the delta function on the right-hand side. Based on the symmetries of the inhomogeneous equation, we construct an invariant fundamental solution in elementary functions. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Differential Equations Springer Journals

Fundamental solution of the elasticity theory equations in displacements for a transversely isotropic medium

Differential Equations , Volume 53 (5) – Jun 14, 2017

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References (8)

Publisher
Springer Journals
Copyright
Copyright © 2017 by Pleiades Publishing, Ltd.
Subject
Mathematics; Ordinary Differential Equations; Partial Differential Equations; Difference and Functional Equations
ISSN
0012-2661
eISSN
1608-3083
DOI
10.1134/S0012266117050056
Publisher site
See Article on Publisher Site

Abstract

We consider a linear fourth-order elliptic partial differential equation describing the displacements of a transversely isotropic linearly elastic medium. We find the symmetries of this equation and of the inhomogeneous equation with the delta function on the right-hand side. Based on the symmetries of the inhomogeneous equation, we construct an invariant fundamental solution in elementary functions.

Journal

Differential EquationsSpringer Journals

Published: Jun 14, 2017

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