Asymptotic behavior of Maxwell's equation in one-space dimension with thermal effect

Yuri Kalinin; Volker Reitmann; Nayil Yumaguzin

doi:10.3934/proc.2011.2011.754

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2011, Volume 2011: 754-762. Doi: 10.3934/proc.2011.2011.754 open access

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Asymptotic behavior of Maxwell's equation in one-space dimension with thermal effect

1.
Department of Mathematics and Mechanics, Saint-Petersburg State University, Saint-Petersburg
2.
Department of Mathematics and Mechanics, Saint-Petersburg State University, Saint-Petersburg, 198504

Received: July 2010

Revised: November 2010

Published: August 2017

Abstract / Introduction Related Papers Cited by

Abstract

A coupled system derived from Maxwell’s equations and the heat transfer equation is considered. For this system with perturbations a cocycle formulation is presented. Using Lyapunov functionals the global stability of the zero solution for the autonomous case is shown. In the case of almost periodic perturbations conditions for the existence of almost periodic solutions are derived.

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Mathematics Subject Classification: 35B15, 35K20, 35K15, 35L20, 80A20.

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