# Exponential decay of quasilinear Maxwell equations with interior conductivity

Lasiecka, Irena; Pokojovy, Michael; Schnaubelt, Roland

Abstract:
We consider a quasilinear nonhomogeneous, anisotropic Maxwell system in a bounded smooth domain $\mathbb{R}$$^{3}$ with a strictly positive conductivity subject to the boundary conditions of a perfect conductor. Under appropriate regularity conditions, adopting a classical L$^{2}$-Sobolev solution
framework, a nonlinear energy barrier estimate is established for local-in-time H$^{3}$-solutions to the Maxwell system by a proper combination of higher-order energy and observability-type estimates under a smallness assumption on the initial data. Technical complications due to quasilinearity, anisotropy and the lack of solenoidality, etc., are addressed. Finally, provided the initial data are small, the barrier method is applied to prove that local solutions exist globally and exhibit an exponential decay rate.

 Zugehörige Institution(en) am KIT Institut für Analysis (IANA)Sonderforschungsbereich 1173 (SFB 1173) Publikationstyp Forschungsbericht Jahr 2018 Sprache Englisch Identifikator ISSN: 2365-662X urn:nbn:de:swb:90-870806 KITopen-ID: 1000087080 Verlag KIT, Karlsruhe Umfang 24 S. Serie CRC 1173 ; 2018/30 Schlagworte Quasilinear Maxwell equations, global existence, boundary conditions of perfect conductor, inhomogeneous anisotropic material laws, exponential stability
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