Local wellposedness of quasilinear Maxwell equations with absorbing boundary conditions

Schnaubelt, Roland; Spitz, Martin

Abstract:
In this article we provide a local wellposedness theory for quasilinear Maxwell equations with absorbing boundary conditions in H$^{m}$ for m≥3. The Maxwell equations are equipped with instantaneous nonlinear material laws leading to a quasilinear symmetric hyperbolic first order system. We consider both linear and nonlinear absorbing boundary conditions. We show existence and uniqueness of a local solution, provide a blow-up criterion in the Lipschitz norm, and prove the continuous dependence on the data. In the case of nonlinear boundary conditions we need a smallness assumption on the tangential trace of the solution. The proof is based on detailed apriori estimates and the regularity theory for the corresponding linear problem which we also develop here.

 Zugehörige Institution(en) am KIT Fakultät für Mathematik (MATH) Publikationstyp Zeitschriftenaufsatz Publikationsjahr 2021 Sprache Englisch Identifikator ISSN: 2163-2480 KITopen-ID: 1000129933 Erschienen in Evolution equations and control theory Verlag American Institute of Mathematical Sciences (AIMS) Band 10 Heft 1 Seiten 155–198 Schlagwörter Nonlinear Maxwell system, absorbing or impedance boundary conditions, local wellposedness, blow-up criterion, continuous dependence Nachgewiesen in ScopusWeb of Science
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