Uniform estimates for transmission problems with high contrast in heat conduction and electromagnetism

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:370

Article

Caloz, Gabriel¹  Dauge, Monique¹  Peron, Victor¹ 

[1] CNRS, Lab IRMAR, UMR 6625, F-35042 Rennes, France

关键词: Maxwell equations;    High conductivity;    Asymptotic expansions;    Lipschitz domains;   

DOI  :  10.1016/j.jmaa.2010.04.060

来源: Elsevier

【 摘 要 】

In this paper we prove uniform a priori estimates for transmission problems with constant coefficients on two subdomains, with a special emphasis for the case when the ratio between these coefficients is large. In the most part of the work, the interface between the two subdomains is supposed to be Lipschitz. We first study a scalar transmission problem which is handled through a converging asymptotic series. Then we derive uniform a priori estimates for Maxwell transmission problem set on a domain made up of a dielectric and a highly conducting material. The technique is based on an appropriate decomposition of the electric field, whose gradient part is estimated thanks to the first part. As an application, we develop an argument for the convergence of an asymptotic expansion as the conductivity tends to infinity. (C) 2010 Elsevier Inc. All rights reserved.

【 授权许可】

Free