MATHEMATICAL ANALYSIS FOR INVERSE PROBLEMS IN CONTINUUM MECHANICS

本研究的目的是对反边值问题及其密切相关的反散射问题的唯一性、稳定性和重构进行理论和数值研究。此外，试图为日本从事反问题研究的研究人员建立一个科学合作网络是另一个目的。为此，获得了以下结果：(1)心电学的理论和数值研究。(2)用探针法识别各向异性弹性介质中的包裹体。(3)介质非均匀性对弹性波逆散射的唯一性。(4)建立残余应力分层剥离法。(5) Dirac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)对边界处的系数及其导数进行局部重构，得到了局部Dirichlet - Neumann映射。(8)声波逆散射问题中障碍物及其阻抗的重构。(9)利用点源重建海洋声学折射率。（10）用切片法重建包体。（11）在平行于时间轴的超曲面上，用解的值及其法向导数重建初始热分布。（12）在半空间中，由调和函数及其范数在与调和函数边界垂直的超平面上的值重建调和函数的边界值。（13）非平稳各向同性弹性方程密度辨识的唯一性和稳定性。（14）在证明电导率反问题的唯一性时，削弱了电导率的正则性假设。（15）多边形腔的有限测量重建。（16）通过出版1998年2月举行的联合研讨会的论文集，努力为从事反问题工作的日韩研究人员建立一个网络。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