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Globalwell-posedness and exponential stability for heterogeneous anisotropic Maxwell’s equations under a nonlinear boundary feedback with delay

Anikushyn, Andrii; Pokojovy, Michael

We consider an initial-boundary value problem for the Maxwell’s system in a bounded domain with a linear inhomogeneous anisotropic instantaneous material law subject to a nonlinear Silver–Müller-type boundary feedback mechanism incorporating both an instantaneous damping and a time-localized delay effect. By proving the maximal monotonicity property of the underlying nonlinear generator, we establish the global well-posedness in an appropriate Hilbert space. Further, under suitable assumptions and geometric conditions, we show the system is exponentially stable.

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Volltext §
DOI: 10.5445/IR/1000084158
Veröffentlicht am 03.07.2018
Zugehörige Institution(en) am KIT Institut für Analysis (IANA)
Publikationstyp Forschungsbericht
Jahr 2018
Sprache Englisch
Identifikator ISSN: 2365-662X
KITopen-ID: 1000084158
Verlag KIT, Karlsruhe
Umfang 24 S.
Serie CRC 1173 ; 2018/10
Schlagworte Maxwell’s equations; nonlinear boundary feedback; instantaneous damping; time-localized delay; well-posedness; exponential stability
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