Cloaking via impedance boundary condition for the 2-D Helmholtz equation

被引：20

作者：

Alekseev, G. V. ^{[1
,2
]}

机构：

[1] Far Eastern Fed Univ, Sch Nat Sci, Vladivostok, Russia

[2] Inst Appl Math FEB RAS, Vladivostok, Russia

来源：

APPLICABLE ANALYSIS | 2014年 / 93卷 / 02期

基金：

俄罗斯基础研究基金会;

关键词：

Helmholtz equation; mixed boundary value problem; impedance; control problem; boundary control; solvability; stability estimates; 35R30; 35Q60; 35J15; 78A25; SCATTERING; SHAPE;

D O I：

10.1080/00036811.2013.768340

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider control problems for the 2-D Helmholtz equation in an unbounded domain with partially coated boundary. Dirichlet boundary condition is given on one part of the boundary and the impedance boundary condition is imposed on another its part. The role of control in control problem under study is played by boundary impedance. Quadratic tracking-type functionals for the field play the role of cost functionals. Solvability of control problems is proved. The uniqueness and stability of optimal solutions with respect to certain perturbations of both cost functional and incident field are established.

引用

页码：254 / 268

页数：15

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