# Boundary stabilization of quasilinear Maxwell equations

Pokojovy, Michael; Schnaubelt, Roland

##### Abstract:
We investigate an initial-boundary value problem for a quasilinear nonhomogeneous, anisotropic Maxwell system subject to an absorbing boundary condition of Silver & Müller type in a smooth, bounded, strictly star-shaped domain of $\mathbb{R^3}$. Imposing usual smallness assumptions in addition to standard regularity and compatibility conditions, a nonlinear stabilizability inequality is obtained by showing nonlinear dissipativity and observability-like estimates enhanced by an intricate regularity analysis. With the stabilizability inequality at hand, the classic nonlinear barrier method
is employed to prove that small initial data admit unique classical solutions that exist globally and decay to zero at an exponential rate. Our approach is based on a ecently established local well-posedness theory in a class of $\mathcal{H}^3$-valued functions.

 Zugehörige Institution(en) am KIT Institut für Analysis (IANA)Sonderforschungsbereich 1173 (SFB 1173) Publikationstyp Forschungsbericht/Preprint Publikationsjahr 2018 Sprache Englisch Identifikator ISSN: 2365-662X urn:nbn:de:swb:90-885994 KITopen-ID: 1000088599 Verlag Karlsruher Institut für Technologie (KIT) Umfang 22 S. Serie CRC 1173 ; 2018/48 Projektinformation SFB 1173/1 (DFG, DFG KOORD, SFB 1173/1 2015) Schlagwörter Maxwell equations, Silver-Müller boundary conditions, nonhomogeneous anisotropic materials, global existence, exponential stability Relationen in KITopen Verweist aufBoundary stabilization of quasilinear Maxwell equations. Pokojovy, Michael; Schnaubelt, Roland (2020) Zeitschriftenaufsatz (1000098430)
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