MATHEMATICAL ANALYSIS FOR INVERSE PROBLEMS IN CONTINUUM MECHANICS

本研究的目的是对逆边值问题及其密切相关的逆散射问题的唯一性、稳定性、重构进行理论和数值研究。此外，另一个目的是试图为在日本从事反问题研究的研究人员建立一个科学合作网络。为此，得到了下列结果：(1)心电信号的理论和数值研究；(2)用探针法识别各向异性弹性介质中的包裹体；(3)弹性波逆散射的唯一性；(4)建立残余应力的剥层方法；(5)狄拉克方程反边值问题和反散射问题的唯一性；(6)确定定常热方程对流项的唯一性；(7)t…边界系数及其导数的局部重建Dirichlet到Neumann映射的局部化。(8)声波反散射问题中障碍物及其阻抗的重建。(9)点源海洋声学折射率的重建。(10)夹杂的切片重建。(11)由平行于时间轴的超曲面上的解及其法向导数的值重建初始热分布。(12)半空间中调和函数边值的重建。(13)唯一性。非定常各向同性弹性方程密度识别的稳定性。(14)在证明电导率反问题的唯一性时弱化电导率的正则性假设。(15)用有限测量重建多边形腔。(16)通过出版1998年2月联合研讨会的会议记录，努力为从事反问题工作的日韩研究人员建立网络。较少

The purpose of this research were the theoretical and numerical studies of the uniqueness, stability, reconstruction for the inverse boundary value problems and their closely related inverse scattering problems. Also, trying to establish a scientific collaboration network for the researchers who are working in inverse problem in Japan was an another purpose. For these purposes the following results were obtained(1) Theoretical and numerical studies of electro-cardiography.(2) Identification of an inclusion in anisotropic elastic medium by the probe method.(3) Uniqueness of the inverse scattering of elastic waves by the inhomogeneity of the medium.(4) Establishing the layer stripping method for residual stress.(5) Uniqueness for the inverse boundary value problem and inverse scattering problem for the Dirac equation.(6) Uniqueness for identifying the convection term for the stationary heat equation.(7) Local reconstruction of the coefficients and their derivatives at the boundary from t … More he localized Dirichlet to Neumann map.(8) Reconstruction of the obstacle and its impedance for the inverse scattering problem for acoustic waves.(9) Reconstruction of the refractive index for ocean acoustics using point sources.(10) Reconstruction of inclusion by the slicing method.(11) Reconstruction of the intitial heat distribution from the value of the solution and its normal derivative on a hypersurface paralle to the time axes.(12) Reconstruction of the boundary value of a harmonic function in the half space from the value of it and its normon a hypeplane perpedicular to the boundary.(13) The uniqueness and stability of identifying the density of the nonstationaly isotropic elastic equation.(14) Weakning the regularity assumption for the conductivity in proving the uniquenss for the inverse conductivity problem.(15) Reconstruction of polygonal cavities by finite measurements.(16) Efforts trying to establish a network for the Japan-Korean researcher working in inverse problems by publishing the proceeding of the joint seminar which was held in Feb. 1998. Less