Stabilization of a Drude/vacuum model. (English) Zbl 1398.35226
Summary: We analyze the stability of a dispersive medium immersed in vacuum (with Silver-Müller boundary condition in the exterior boundary) or vice versa. The dispersive medium model corresponds to the coupling between Maxwell’s system and a first order ordinary differential equation (of parabolic type). For a dispersive medium coupled with vacuum, the ordinary differential equation will be set in a subset of the full domain. We show that this model is well-posed and is strongly stable in a closed subspace of the energy space. We further identify some sufficient conditions that guarantee the exponential or polynomial decay of the associated energy in this subspace.
MSC:
35Q60 | PDEs in connection with optics and electromagnetic theory |
35L15 | Initial value problems for second-order hyperbolic equations |
93D15 | Stabilization of systems by feedback |
35B35 | Stability in context of PDEs |
35B40 | Asymptotic behavior of solutions to PDEs |
35P05 | General topics in linear spectral theory for PDEs |