Well-posedness and exponential stability of nonlinear Maxwell equations for dispersive materials with interface. (English) Zbl 1532.35440
Authors’ abstract: In this paper we consider an abstract Cauchy problem for a Maxwell system modeling 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.
Reviewer: Guido Schneider (Stuttgart)
MSC:
| 35Q61 | Maxwell equations |
| 78A60 | Lasers, masers, optical bistability, nonlinear optics |
| 78A48 | Composite media; random media in optics and electromagnetic theory |
| 35R09 | Integro-partial differential equations |
| 35B35 | Stability in context of PDEs |
| 35A01 | Existence problems for PDEs: global existence, local existence, non-existence |
| 35A02 | Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness |
Keywords:
Maxwell equations in nonlinear optics; evolutionary equations; exponential stability; exponentially weighted spaces; material interfacesReferences:
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