Local wellposedness of nonlinear Maxwell equations with perfectly conducting boundary conditions

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:266

Article

Spitz, Martin¹ 

[1] Karlsruhe Inst Technol, Dept Math, Englerstr 2, D-76131 Karlsruhe, Germany

关键词: Nonlinear Maxwell equations;    Perfectly conducting boundary conditions;    Quasilinear initial boundary value problem;    Hyperbolic system;    Local wellposedness;    Continuous dependence;   

DOI  :  10.1016/j.jde.2018.10.019

来源: Elsevier

【 摘 要 】

In this article we develop the local wellposedness theory for quasilinear Maxwell equations in H-m for all m >= 3 on domains with perfectly conducting boundary conditions. The macroscopic Maxwell equations with instantaneous material laws for the polarization and the magnetization lead to a quasilinear first order hyperbolic system whose wellposedness in H-3 is not covered by the available results in this case. We prove the existence and uniqueness of local solutions in H-m with m >= 3 of the corresponding initial boundary value problem if the material laws and the data are accordingly regular and compatible. We further characterize finite time blowup in terms of the Lipschitz norm and we show that the solutions depend continuously on their data. Finally, we establish the finite propagation speed of the solutions. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free