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Decay rates for solutions of a Maxwell system with nonlinear boundary damping. (English) Zbl 1119.93402

Summary: The purpose of this paper is to obtain decay rates for the electromagnetic energy of solutions of a dynamic Maxwell system with spatially varying dielectric constant \(\varepsilon\) and magnetic permeability \(\mu\) in a bounded, connected domain \(\Omega\). Dissipation is introduced into the system through a nonlinear Silver-Müller boundary condition. A general result on energy decay is proved when \(\partial\Omega\in C^\infty\) and consists of a single connected component, and \(\varepsilon,\mu\) are of class \(C^\infty(\overline \Omega)\) and satisfy a certain technical condition. Examples are provided that illustrate the general result and, in particular, it is shown how dissipative boundary conditions may be constructed that lead to a specified energy decay rate.

MSC:

93D15 Stabilization of systems by feedback
35Q60 PDEs in connection with optics and electromagnetic theory
35L50 Initial-boundary value problems for first-order hyperbolic systems
93C20 Control/observation systems governed by partial differential equations
93C10 Nonlinear systems in control theory
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