CLOAKING FOR A QUASI-LINEAR ELLIPTIC PARTIAL DIFFERENTIAL EQUATION

被引：1

作者：

Ghosh, Tuhin ^{[1
]}

Iyer, Karthik ^{[2
]}

机构：

[1] Hong Kong Univ Sci & Technol, Jockey Club Inst Adv Study, Hong Kong, Peoples R China

[2] Univ Washington, Dept Math, Seattle, WA 98195 USA

来源：

INVERSE PROBLEMS AND IMAGING | 2018年 / 12卷 / 02期

关键词：

Quasilinear elliptic; homogenization; cloaking; inverse problems; INVERSE CONDUCTIVITY PROBLEM; ELECTROMAGNETIC WORMHOLES; GLOBAL UNIQUENESS; INVISIBILITY; DEVICES; FULL;

D O I：

10.3934/ipi.2018020

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this article we consider cloaking for a quasi-linear elliptic partial differential equation of divergence type de fined on a bounded domain in R-N for N = 2, 3. We show that a perfect cloak can be obtained via a singular change of variables scheme and an approximate cloak can be achieved via a regular change of variables scheme. These approximate cloaks, though non-degenerate, are anisotropic. We also show, within the framework of homogenization, that it is possible to get isotropic regular approximate cloaks. This work generalizes to quasi-linear settings previous work on cloaking in the context of Electrical Impedance Tomography for the conductivity equation.

引用

页码：461 / 491

页数：31

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