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

Pages: 407 - 414, Issue special, November 2013

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Dina Kalinichenko - Department of Mathematics and Mechanics, Saint-Petersburg State University, Saint-Petersburg, 198504, Russian Federation (email)
Volker Reitmann - Department of Mathematics and Mechanics, Saint-Petersburg State University, Saint-Petersburg, 198504, Russian Federation (email)
Sergey Skopinov - Department of Mathematics and Mechanics, Saint-Petersburg State University, Saint-Petersburg, 198504, Russian Federation (email)

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.

Keywords:  Asymptotic behavior, evolutionary variational inequality, stability, dissipativity, frequency-domain condition, Maxwell's equation.
Mathematics Subject Classification:  Primary: 35B35, 35B40; Secondary: 35K15, 35L20, 80A20.

Received: September 2012; Published: November 2013.

 References