Eller, M.; Lagnese, J. E.; Nicaise, S. Decay rates for solutions of a Maxwell system with nonlinear boundary damping. (English) Zbl 1119.93402 Comput. Appl. Math. 21, No. 1, 135-165 (2002). 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. Cited in 35 Documents 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 Keywords:energy decay rates; nonlinear Silver-Müller boundary condition PDFBibTeX XMLCite \textit{M. Eller} et al., Comput. Appl. Math. 21, No. 1, 135--165 (2002; Zbl 1119.93402)