Study of Inverse Problems for Family of Elasticity Equations

对非侵入性测量活体组织粘弹性的弹性成像的数据分析进行了一些研究，并获得了足够的结果，作为其相关研究，抛物方程的LSM（线性采样方法）和反常扩散方程的Carleman估计。我们完成了近几年来关于半空间深度相关的各向异性弹性介质中瑞利波速度频散公式的研究。提出了钢-混凝土组合梁连接件损伤检测的反演方法。

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.