Well-Posedness and Exponential Stability of Nonlinear Maxwell Equations for Dispersive Materials with Interface
Analysis of PDEs
2023-11-21 v3
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.
Cite
@article{arxiv.2301.10099,
title = {Well-Posedness and Exponential Stability of Nonlinear Maxwell Equations for Dispersive Materials with Interface},
author = {Tomáš Dohnal and Mathias Ionescu-Tira and Marcus Waurick},
journal= {arXiv preprint arXiv:2301.10099},
year = {2023}
}