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

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


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