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Open AccessArticle

Symmetry Analysis and Conservation Laws of a Generalization of the Kelvin-Voigt Viscoelasticity Equation

Department of Mathematics, University of Cadiz, Facultad de Ciencias Campus del Río San Pedro, 11510 Puerto Real, Spain
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Symmetry 2019, 11(7), 840; https://doi.org/10.3390/sym11070840
Received: 30 May 2019 / Revised: 22 June 2019 / Accepted: 24 June 2019 / Published: 28 June 2019
(This article belongs to the Special Issue Noether's Theorem and Symmetry)
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PDF [251 KB, uploaded 28 June 2019]

Abstract

In this paper, we study a generalization of the well-known Kelvin-Voigt viscoelasticity equation describing the mechanical behaviour of viscoelasticity. We perform a Lie symmetry analysis. Hence, we obtain the Lie point symmetries of the equation, allowing us to transform the partial differential equation into an ordinary differential equation by using the symmetry reductions. Furthermore, we determine the conservation laws of this equation by applying the multiplier method. View Full-Text
Keywords: viscoelasticity; Kelvin-Voigt equation; Lie symmetries; optimal system; group-invariant solutions; conservation laws; multiplier method viscoelasticity; Kelvin-Voigt equation; Lie symmetries; optimal system; group-invariant solutions; conservation laws; multiplier method
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Márquez, A.P.; Bruzón, M.S. Symmetry Analysis and Conservation Laws of a Generalization of the Kelvin-Voigt Viscoelasticity Equation. Symmetry 2019, 11, 840.

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