Study of Inverse Problems for Family of Elasticity Equations

在非侵入性测量活体组织粘弹性的弹性学数据分析以及与之相关的抛物方程线性抽样法和异常扩散方程Carleman估计等方面进行了一些研究，并取得了充分的结果。我们完成了近年来对半空间深度相关的各向异性残余应力介质中瑞利波速度频散公式的研究。给出了钢-混凝土组合梁连接件损伤检测的反演方案。

Some studies were done and obtained sufficient results on the data analysis of elastography which measures the visco-elasticity of tissues in a living body non-invasively, and as their related studies, the LSM (linear sampling method) for parabolic equations and Carleman estimate for anomalous diffusion equations. We completed our recent year study on the dispersion formula of the speed of Rayleigh wave for half space depth dependent anisotrpic elastic media with residual stress. We gave an inversion scheme for detecting damage of connectors of steel-concrete composite beam.