Identification problems in linear elasticity

Hyunseok Kim; Jin Keun Seo

doi:10.1006/jmaa.1997.5656

Identification problems in linear elasticity

Hyunseok Kim, Jin Keun Seo

Department of Computational Science and Engineering

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

2 Citations (Scopus)

Abstract

Let Ω be a bounded domain inRⁿwithC²-boundary and letDbe a Lipschitz domain withD⊂Ω. We consider the inverse problem (determiningD) to the system of linear elasticityD_i((μ_D(δ_ijδ_rs+δ_irδ_js)+λ_Dδ_irδ_js)D_ju^s)=0in Ω,where μ_D=μ_χD+μ_χRn\Dand λ_D=λ_χD+λ_χRn\D. Under the condition on the Lamè constants (λ-λ)(μ-μ)≥0, we show thatDis uniquely determined by the complete knowledge of the Dirichlet-to-Neumann map. We also obtain an uniqueness result for the monotone case from one boundary measurement.

Original language	English
Pages (from-to)	514-531
Number of pages	18
Journal	Journal of Mathematical Analysis and Applications
Volume	215
Issue number	2
DOIs	https://doi.org/10.1006/jmaa.1997.5656
Publication status	Published - 1997 Nov 15

Bibliographical note

Funding Information:
We thank the referee for several comments. The second author is supported in part by GARC-KOSEF, BSRI96-0701-04-01-3, and IMS at Yonsei University.

All Science Journal Classification (ASJC) codes

Analysis
Applied Mathematics

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10.1006/jmaa.1997.5656

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title = "Identification problems in linear elasticity",

abstract = "Let Ω be a bounded domain inRnwithC2-boundary and letDbe a Lipschitz domain withD⊂Ω. We consider the inverse problem (determiningD) to the system of linear elasticityDi((μD(δijδrs+δirδjs)+λDδirδjs)Djus)=0in Ω,where μD=μχD+μχRn\Dand λD=λχD+λχRn\D. Under the condition on the Lam{\`e} constants (λ-λ)(μ-μ)≥0, we show thatDis uniquely determined by the complete knowledge of the Dirichlet-to-Neumann map. We also obtain an uniqueness result for the monotone case from one boundary measurement.",

author = "Hyunseok Kim and Seo, {Jin Keun}",

note = "Funding Information: We thank the referee for several comments. The second author is supported in part by GARC-KOSEF, BSRI96-0701-04-01-3, and IMS at Yonsei University.",

year = "1997",

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doi = "10.1006/jmaa.1997.5656",

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journal = "Journal of Mathematical Analysis and Applications",

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AU - Kim, Hyunseok

AU - Seo, Jin Keun

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PY - 1997/11/15

Y1 - 1997/11/15

N2 - Let Ω be a bounded domain inRnwithC2-boundary and letDbe a Lipschitz domain withD⊂Ω. We consider the inverse problem (determiningD) to the system of linear elasticityDi((μD(δijδrs+δirδjs)+λDδirδjs)Djus)=0in Ω,where μD=μχD+μχRn\Dand λD=λχD+λχRn\D. Under the condition on the Lamè constants (λ-λ)(μ-μ)≥0, we show thatDis uniquely determined by the complete knowledge of the Dirichlet-to-Neumann map. We also obtain an uniqueness result for the monotone case from one boundary measurement.

AB - Let Ω be a bounded domain inRnwithC2-boundary and letDbe a Lipschitz domain withD⊂Ω. We consider the inverse problem (determiningD) to the system of linear elasticityDi((μD(δijδrs+δirδjs)+λDδirδjs)Djus)=0in Ω,where μD=μχD+μχRn\Dand λD=λχD+λχRn\D. Under the condition on the Lamè constants (λ-λ)(μ-μ)≥0, we show thatDis uniquely determined by the complete knowledge of the Dirichlet-to-Neumann map. We also obtain an uniqueness result for the monotone case from one boundary measurement.

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