Regularity theory for nonautonomous Maxwell equations with perfectly conducting boundary conditions

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:506

Article

Spitz, Martin¹ 

[1] Univ Bielefeld, Fak Math, Postfach 10 01 31, D-33501 Bielefeld, Germany

关键词: Maxwell equations;    Perfectly conducting boundary conditions;    Hyperbolic system;    Initial boundary value problem;    Characteristic boundary;    Regularity theory;   

DOI  :  10.1016/j.jmaa.2021.125646

来源: Elsevier

【 摘 要 】

In this work we study linear Maxwell equations with time-and space-dependent matrix-valued permittivity and permeability on domains with a perfectly conducting boundary. This leads to an initial boundary value problem for a first-order hyperbolic system with characteristic boundary. We prove a priori estimates for solutions in H-m. Moreover, we show the existence of a unique H-m-solution if the coefficients and the data are sufficiently regular and satisfy certain compatibility conditions. Since the boundary is characteristic for the Maxwell system, we have to exploit the divergence conditions in the Maxwell equations in order to derive the energy-type H-m-estimates. A combination of these estimates with several regularization techniques then yields the existence of solutions in H-m. (C) 2021 Elsevier Inc. All rights reserved.

【 授权许可】

Free