Uniqueness in inverse problems for an elasticity system with residual stress by a single measurement

Ching Lung Lin; Jenn Nan Wang

doi:10.1088/0266-5611/19/4/301

Uniqueness in inverse problems for an elasticity system with residual stress by a single measurement

Ching Lung Lin, Jenn Nan Wang

Department of Mathematics

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

13 Citations (Scopus)

Abstract

In this paper we consider an elasticity system with residual stress. The constitutive equation of this elasticity system differs from that of the isotropic elasticity system by R + (∇u) R, where R is the residual stress tensor. This system is not isotropic due to the existence of the residual stress R. Thus, it is not possible to reduce the principal part of the system to uncoupled wave operators as we have for the isotropic elasticity system. Here we investigate inverse problems of identifying the force term or the density by a single measurement of the lateral boundary. We establish uniqueness results by means of Carleman estimates when the residual stress is small.

Original language	English
Pages (from-to)	807-820
Number of pages	14
Journal	Inverse Problems
Volume	19
Issue number	4
DOIs	https://doi.org/10.1088/0266-5611/19/4/301
Publication status	Published - 2003 Aug

All Science Journal Classification (ASJC) codes

Theoretical Computer Science
Signal Processing
Mathematical Physics
Computer Science Applications
Applied Mathematics

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AB - In this paper we consider an elasticity system with residual stress. The constitutive equation of this elasticity system differs from that of the isotropic elasticity system by R + (∇u) R, where R is the residual stress tensor. This system is not isotropic due to the existence of the residual stress R. Thus, it is not possible to reduce the principal part of the system to uncoupled wave operators as we have for the isotropic elasticity system. Here we investigate inverse problems of identifying the force term or the density by a single measurement of the lateral boundary. We establish uniqueness results by means of Carleman estimates when the residual stress is small.

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Uniqueness in inverse problems for an elasticity system with residual stress by a single measurement

Abstract

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