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

Pages: 754 - 762, Issue Special, September 2011

 Abstract        Full Text (734.8K)              

Yuri Kalinin - Department of Mathematics and Mechanics, Saint-Petersburg State University, Saint-Petersburg, Russian Federation (email)
Volker Reitmann - Department of Mathematics and Mechanics, Saint-Petersburg State University, Saint-Petersburg, 198504, Russian Federation (email)
Nayil Yumaguzin - Department of Mathematics and Mechanics, Saint-Petersburg State University, Saint-Petersburg, Russian Federation (email)

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.

Keywords:  Maxwell’s equation, thermal effect, global stability, almost periodic solution
Mathematics Subject Classification:  35B15, 35K20, 35K15, 35L20, 80A20

Received: July 2010;      Revised: November 2010;      Published: October 2011.