Cloaking for a quasi-linear elliptic partial differential equation

Tuhin Ghosh; Karthik Iyer

doi:10.3934/ipi.2018020

Article Contents

2018, Volume 12, Issue 2: 461-491. Doi: 10.3934/ipi.2018020

This issue Previous Article Efficient tensor tomography in fan-beam coordinates. Ⅱ: Attenuated transforms Next Article A globally convergent numerical method for a 3D coefficient inverse problem with a single measurement of multi-frequency data

Cloaking for a quasi-linear elliptic partial differential equation

Tuhin Ghosh^1, and
Karthik Iyer^2,

1.
Jockey Club Institute for Advanced Study, Hong Kong University of Science and Technology, Hong Kong, China
2.
Department of Mathematics, University of Washington, Seattle, WA 98195-4350, USA

Received: June 2017

Revised: September 2017

Published: April 2018

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Abstract

In this article we consider cloaking for a quasi-linear elliptic partial differential equation of divergence type defined on a bounded domain in $\mathbb{R}^N$ 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.

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Mathematics Subject Classification: Primary: 35R30; Secondary: 35J62.

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