Stability properties for a problem of light scattering in a dispersive metallic domain

Serge Nicaise (1) , Claire Scheid (2, 3)

1 UPHF - Université Polytechnique Hauts-de-France
2 UniCA - Université Côte d'Azur
3 ATLANTIS - Modélisation et méthodes numériques pour le calcul d'interactions onde-matière nanostructurée

In this work, we study the well-posedness and some stability properties of a PDE system that models the propagation of light in a metallic domain with a hole. This model takes into account the dispersive properties of the metal. It consists of a linear coupling between Maxwell's equations and a wave type system. We prove that the problem is well posed for several types of boundary conditions. Furthermore, we show that it is polynomially stable and that the exponential stability is conditional on the exponential stability of the Maxwell system.

Mots clés: Maxwell's equation; Stability analysis; dispersive media

Domaines: Mathématiques [math]

Serge Nicaise, Claire Scheid. Stability properties for a problem of light scattering in a dispersive metallic domain. Evolution Equations and Control Theory, 2023, 12 (1), pp.20. ⟨10.3934/eect.2022020⟩. ⟨hal-03540550⟩