Nonlinear waves in thermoelastic dielectrics

Angelo Morro

doi:10.3934/eect.2019009

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2019, Volume 8, Issue 1: 149-162. Doi: 10.3934/eect.2019009

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Nonlinear waves in thermoelastic dielectrics

Angelo Morro

DIBRIS, University of Genoa, 16145 Genoa, Italy

The research leading to this paper has been developed under the auspices of INDAM, Italy

Received: November 30, 2017

Revised: January 31, 2018

Early access: December 2018

Published: January 2019

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Abstract

This paper is addressed to the analysis of wave propagation in electroelastic materials. First the balance equations are reviewed and the entropy inequality is established. Next the constitutive equations are considered for a deformable and heat-conducting dielectric. To allow for discontinuity wave propagation, an appropriate objective rate equation of the heat flux is considered. The thermodynamic consistency of the whole set of constitutive equations is established. Next the nonlinear evolution equations so determined are tested in relation to wave propagation properties. Waves are investigated in the form of weak discontinuities and the whole system of equations for the jumps is obtained. As a particular simple case the propagation into an unperturbed region is examined. Both the classical electromagnetic waves and the thermal waves are found to occur. In both cases the mechanical term is found to be induced by the electrical or the thermal wave discontinuity.

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Mathematics Subject Classification: Primary: 74B20, 74F15, 74F05; Secondary: 78A25.

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