On stability for a translated obstacle with impedance boundary condition

Jijun Liu; Jinkeun Seo

doi:10.1016/j.na.2004.07.033

On stability for a translated obstacle with impedance boundary condition

Jijun Liu, Jinkeun Seo

Department of Computational Science and Engineering

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

19 Citations (Scopus)

Abstract

This paper considers an inverse problem of determining the location of a known obstacle and its boundary impedance from one or two incident waves. We firstly derive a concrete formula of the far-field pattern due to a translation of the obstacle and perturbation of its boundary impedance. Based on this formula, we establish Lipschitz stability for the recovery of translation of an obstacle with one incident wave. In the special case of obstacle being a ball, Lipschitz stability for the recovery of both location and its boundary coefficient can be obtained using two incident waves.

Original language	English
Pages (from-to)	731-744
Number of pages	14
Journal	Nonlinear Analysis, Theory, Methods and Applications
Volume	59
Issue number	5
DOIs	https://doi.org/10.1016/j.na.2004.07.033
Publication status	Published - 2004 Nov

Bibliographical note

Funding Information:
This is a project supported by NSFC (10371018). The first named author thanks Yonsei University for its hospitality during his visiting. The authors also wish to express their thanks to the referees for their helpful suggestions.

All Science Journal Classification (ASJC) codes

Analysis
Applied Mathematics

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10.1016/j.na.2004.07.033

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title = "On stability for a translated obstacle with impedance boundary condition",

abstract = "This paper considers an inverse problem of determining the location of a known obstacle and its boundary impedance from one or two incident waves. We firstly derive a concrete formula of the far-field pattern due to a translation of the obstacle and perturbation of its boundary impedance. Based on this formula, we establish Lipschitz stability for the recovery of translation of an obstacle with one incident wave. In the special case of obstacle being a ball, Lipschitz stability for the recovery of both location and its boundary coefficient can be obtained using two incident waves.",

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author = "Jijun Liu and Jinkeun Seo",

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AU - Liu, Jijun

AU - Seo, Jinkeun

N1 - Funding Information: This is a project supported by NSFC (10371018). The first named author thanks Yonsei University for its hospitality during his visiting. The authors also wish to express their thanks to the referees for their helpful suggestions.

PY - 2004/11

Y1 - 2004/11

N2 - This paper considers an inverse problem of determining the location of a known obstacle and its boundary impedance from one or two incident waves. We firstly derive a concrete formula of the far-field pattern due to a translation of the obstacle and perturbation of its boundary impedance. Based on this formula, we establish Lipschitz stability for the recovery of translation of an obstacle with one incident wave. In the special case of obstacle being a ball, Lipschitz stability for the recovery of both location and its boundary coefficient can be obtained using two incident waves.

AB - This paper considers an inverse problem of determining the location of a known obstacle and its boundary impedance from one or two incident waves. We firstly derive a concrete formula of the far-field pattern due to a translation of the obstacle and perturbation of its boundary impedance. Based on this formula, we establish Lipschitz stability for the recovery of translation of an obstacle with one incident wave. In the special case of obstacle being a ball, Lipschitz stability for the recovery of both location and its boundary coefficient can be obtained using two incident waves.

KW - Inverse scattering

KW - Nonlinearity

KW - Stability

KW - Uniqueness

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SN - 0362-546X

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SP - 731

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JO - Nonlinear Analysis, Theory, Methods and Applications

JF - Nonlinear Analysis, Theory, Methods and Applications

IS - 5

ER -

On stability for a translated obstacle with impedance boundary condition

Abstract

Bibliographical note

All Science Journal Classification (ASJC) codes

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