Recovering an obstacle using integral equations

William Rundell

doi:10.3934/ipi.2009.3.319

Recovering an obstacle using integral equations

William Rundell

Research output: Contribution to journal › Article › peer-review

Abstract

We consider the inverse problem of recovering the shape, location and surface properties of an object where the surrounding medium is both conductive and homogeneous and we measure Cauchy data on an accessible part of the exterior boundary. It is assumed that the physical situation is modelled by harmonic functions and the boundary condition on the obstacle is one of Dirichlet type. The purpose of this paper is to answer some of the questions raised in a recent paper that introduced a nonlinear integral equation approach for the solution of this type of problem.

Original language	English (US)
Pages (from-to)	319-332
Number of pages	14
Journal	Inverse Problems and Imaging
Volume	3
Issue number	2
DOIs	https://doi.org/10.3934/ipi.2009.3.319
State	Published - May 14 2009
Externally published	Yes

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUS-CI-016-04
Acknowledgements: This research was partially supported by the National Science Foundation under grant DMS-0715060 and by the King Abdullah University of Science and Technology (KAUST) under awardKUS-CI-016-04.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.

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10.3934/ipi.2009.3.319

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title = "Recovering an obstacle using integral equations",

abstract = "We consider the inverse problem of recovering the shape, location and surface properties of an object where the surrounding medium is both conductive and homogeneous and we measure Cauchy data on an accessible part of the exterior boundary. It is assumed that the physical situation is modelled by harmonic functions and the boundary condition on the obstacle is one of Dirichlet type. The purpose of this paper is to answer some of the questions raised in a recent paper that introduced a nonlinear integral equation approach for the solution of this type of problem.",

author = "William Rundell",

note = "KAUST Repository Item: Exported on 2020-10-01 Acknowledged KAUST grant number(s): KUS-CI-016-04 Acknowledgements: This research was partially supported by the National Science Foundation under grant DMS-0715060 and by the King Abdullah University of Science and Technology (KAUST) under awardKUS-CI-016-04. This publication acknowledges KAUST support, but has no KAUST affiliated authors.",

year = "2009",

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PY - 2009/5/14

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N2 - We consider the inverse problem of recovering the shape, location and surface properties of an object where the surrounding medium is both conductive and homogeneous and we measure Cauchy data on an accessible part of the exterior boundary. It is assumed that the physical situation is modelled by harmonic functions and the boundary condition on the obstacle is one of Dirichlet type. The purpose of this paper is to answer some of the questions raised in a recent paper that introduced a nonlinear integral equation approach for the solution of this type of problem.

AB - We consider the inverse problem of recovering the shape, location and surface properties of an object where the surrounding medium is both conductive and homogeneous and we measure Cauchy data on an accessible part of the exterior boundary. It is assumed that the physical situation is modelled by harmonic functions and the boundary condition on the obstacle is one of Dirichlet type. The purpose of this paper is to answer some of the questions raised in a recent paper that introduced a nonlinear integral equation approach for the solution of this type of problem.

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UR - http://aimsciences.org//article/doi/10.3934/ipi.2009.3.319

U2 - 10.3934/ipi.2009.3.319

DO - 10.3934/ipi.2009.3.319

M3 - Article

SN - 1930-8337

VL - 3

SP - 319

EP - 332

JO - Inverse Problems and Imaging

JF - Inverse Problems and Imaging

IS - 2

ER -

Recovering an obstacle using integral equations

Abstract

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