CONSTRUCTIVE FORMULATIONS OF RESONANT MAXWELL'S EQUATIONS

被引：9

作者：

Pinto, M. Campos ^{[1
]}

Despres, B. ^{[1
]}

机构：

[1] UPMC Univ Paris 06, Sorbonne Univ, CNRS, UMR 7598,Lab Jacques Louis Lions, F-75005 Paris, France

来源：

SIAM JOURNAL ON MATHEMATICAL ANALYSIS | 2017年 / 49卷 / 05期

关键词：

Maxwell's equations; singular solutions; resonant dielectric tensor; resonant heating; limit absorption principle; manufactured solutions; ABSORPTION; INTERFACE; PLASMAS; FINITE; CORNER;

D O I：

10.1137/16M1063198

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this article we propose new constructive weak formulations for resonant time harmonic wave equations with singular solutions. Our approach follows the limiting absorption principle and combines standard weak formulations of PDEs with properties of elementary special functions adapted to the singularity of the solutions, called manufactured solutions. We show the well-posedness of several formulations obtained by these means for the limit problem in dimension one, and propose a generalization in dimension two.

引用

页码：3637 / 3670

页数：34

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