Carleman estimate for a stationary isotropic Lamé system and the applications
Carleman estimate for a stationary isotropic Lamé system and the applications
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DOI：
10.1080/00036810310001632772
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发表时间：
2004-03
影响因子：
1.1
通讯作者：
O. Imanuvilov;Masahiro Yamamoto
中科院分区：
文献类型：
--
作者：
O. Imanuvilov;Masahiro Yamamoto
对于具有Dirichlet边界条件或表面应力边界条件的各向同性定常Lamé系统，我们得到了如下的Carleman估计：(1)在加权L 2-空间中估计右侧；(2)估计包含非齐次表面位移或表面应力.利用这个估计，我们通过在任意子区域上的测量或在任意子边界上的表面位移和应力的测量，建立了位移的Sobolev范数的条件稳定性。最后，利用Carleman估计，我们证明了由一次内部测量确定源项反问题的唯一性和条件稳定性。
For the isotropic stationary Lamé system with variable coefficients equipped with the Dirichlet or surface stress boundary condition, we obtain a Carleman estimate such that (i) the right hand side is estimated in a weighted L 2-space and (ii) the estimate includes nonhomogeneous surface displacement or surface stress. Using this estimate we establish the conditional stability in Sobolev's norm of the displacement by means of measurements in an arbitrary subdomain or measurements of surface displacement and stress on an arbitrary subboundary. Finally by the Carleman estimate, we prove the uniqueness and conditional stability for an inverse problem of determining a source term by a single interior measurement.