INCOMING AND DISAPPEARING SOLUTIONS FOR MAXWELL'S EQUATIONS

被引：6

作者：

Colombini, Ferruccio ^{[1
]}

Petkov, Vesselin ^{[2
]}

Rauch, Jeffrey ^{[3
]}

机构：

[1] Univ Pisa, Dipartimento Matemat, I-56100 Pisa, Italy

[2] Inst Math Bordeaux, F-33405 Talence, France

[3] Univ Michigan, Dept Math, Ann Arbor, MI 48109 USA

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2011年 / 139卷 / 06期

基金：

美国国家科学基金会;

关键词：

Maxwell equations; disappearing solutions; dissipative boundary conditions;

D O I：

10.1090/S0002-9939-2011-10885-2

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove that in contrast to the free wave equation in R(3) there are no incoming solutions of Maxwell's equations in the form of spherical or modulated spherical waves. We construct solutions which are corrected by lower order incoming waves. With their aid, we construct dissipative boundary conditions and solutions to Maxwell's equations in the exterior of a sphere which decay exponentially as t -> +infinity. They are asymptotically disappearing. Disappearing solutions which are identically zero for t >= T > 0 are constructed which satisfy maximal dissipative boundary conditions which depend on time t. Both types are invisible in scattering theory.

引用

页码：2163 / 2173

页数：11

共 5 条

[1] SYMMETRIC POSITIVE LINEAR DIFFERENTIAL EQUATIONS [J].

FRIEDRICHS, KO .

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1958, 11 (03) :333-418

[2]

Georgiev V., 1986, HOKKAIDO MATH J, V15, P357

[3] LOCAL BOUNDARY CONDITIONS FOR DISSIPATIVE SYMMETRIC LINEAR DIFFERENTIAL OPERATORS [J].

LAX, PD ;

PHILLIPS, RS .

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1960, 13 (03) :427-455

[4]

MAJDA A, 1974, INDIANA U MATH J, V24, P1119

[5]

Petkov V., 1989, Scattering Theory for Hyperbolic Operators

← 1 →