Asymptotic behavior of solutions to a coupled system of Maxwell’s equations and a controlled differential inclusion. (English) Zbl 1308.35297
Summary: 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.
MSC:
35Q61 | Maxwell equations |
35B35 | Stability in context of PDEs |
35B40 | Asymptotic behavior of solutions to PDEs |
35K15 | Initial value problems for second-order parabolic equations |
35L20 | Initial-boundary value problems for second-order hyperbolic equations |
80A20 | Heat and mass transfer, heat flow (MSC2010) |