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2011, 2011(Special): 754-762. doi: 10.3934/proc.2011.2011.754

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

Yuri Kalinin 1, , Volker Reitmann 2, and  Nayil Yumaguzin 1,

1. 

Department of Mathematics and Mechanics, Saint-Petersburg State University, Saint-Petersburg, Russian Federation, Russian Federation
2. 

Department of Mathematics and Mechanics, Saint-Petersburg State University, Saint-Petersburg, 198504, Russian Federation

Received  July 2010 Revised  November 2010 Published  October 2011

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.
Keywords: thermal effect, global stability, Maxwell’s equation, almost periodic solution.
Mathematics Subject Classification: 35B15, 35K20, 35K15, 35L20, 80A20.
Citation: Yuri Kalinin, Volker Reitmann, Nayil Yumaguzin. Asymptotic behavior of Maxwell's equation in one-space dimension with thermal effect. Conference Publications, 2011, 2011 (Special) : 754-762. doi: 10.3934/proc.2011.2011.754
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