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arXiv · 2301.10099

Well-Posedness and Exponential Stability of Nonlinear Maxwell Equations for Dispersive Materials with Interface

Tomáš Dohnal·Mathias Ionescu-Tira·Marcus Waurick
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Abstract

In this paper we consider an abstract Cauchy problem for a Maxwell system modelling electromagnetic fields in the presence of an interface between optical media. The electric polarization is in general time-delayed and nonlinear, turning the macroscopic Maxwell equations into a system of nonlinear integro-differential equations. Within the framework of evolutionary equations, we obtain well-posedness in function spaces exponentially weighted in time and of different spatial regularity and formulate various conditions on the material functions, leading to exponential stability on a bounded domain.

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Tomáš Dohnal, Mathias Ionescu-Tira, Marcus Waurick. 2023-01-24. Well-Posedness and Exponential Stability of Nonlinear Maxwell Equations for Dispersive Materials with Interface. https://doi.org/10.1016/j.jde.2023.11.005

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