Asymptotic behavior of solutions to a coupled system of Maxwell's equations and a controlled differential inclusion

Dina Kalinichenko; Volker Reitmann; Sergey Skopinov

doi:10.3934/proc.2013.2013.407

Article Contents

2013, Volume 2013: 407-414. Doi: 10.3934/proc.2013.2013.407 open access

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Asymptotic behavior of solutions to a coupled system of Maxwell's equations and a controlled differential inclusion

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

Received: September 2012

Published: November 2013

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Abstract

The present article consists of two parts. In the first part we consider evolutionary variational inequalities with a nonlinearity which is described by a differential inclusion. Using the frequency-domain method we prove, under certain assumptions, the dissipativity of our variational inequality which is important for the asymptotic behavior of the system. In the second part a coupled system of Maxwell's equation and the heat equation is considered. For this system we introduce the notion of stability on a finite-time interval and present a theorem on this type of stability.

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Mathematics Subject Classification: Primary: 35B35, 35B40; Secondary: 35K15, 35L20, 80A20.

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References

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