Identification problems in linear elasticity

Hyunseok Kim, Jin Keun Seo

Research output: Contribution to journalArticle

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 elasticityDi((μDijδrsirδjs)+λDδirδjs)Djus)=0in Ω,where μDχDχRn\Dand λDχDχRn\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 languageEnglish
Pages (from-to)514-531
Number of pages18
JournalJournal of Mathematical Analysis and Applications
Volume215
Issue number2
DOIs
Publication statusPublished - 1997 Nov 15

Fingerprint

Linear Elasticity
Identification Problem
Inverse problems
Elasticity
Dirichlet-to-Neumann Map
Lipschitz Domains
Bounded Domain
Monotone
Inverse Problem
Uniqueness
Knowledge

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

Cite this

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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.",
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Identification problems in linear elasticity. / Kim, Hyunseok; Seo, Jin Keun.

In: Journal of Mathematical Analysis and Applications, Vol. 215, No. 2, 15.11.1997, p. 514-531.

Research output: Contribution to journalArticle

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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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