MATHEMATICAL ANALYSIS FOR INVERSE PROBLEMS IN CONTINUUM MECHANICS

连续力学反问题的数学分析

• 批准号: 10640152
• 负责人: NAKAMURA Gen
• 金额: $ 1.09万
• 依托单位: Gunma University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 1998
• 资助国家: 日本
• 起止时间: 1998 至 1999
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-10640152/
• 关键词: INVERSE PROBLEMS; ELASTIC EQUATION; LAYER STRIPPING; INVERSE SCATTERING; PROBE MEHOD; RESIDUAL STRESS; DIRAC EQUATION; DIRICHLET TO NEUMANN MAP; 海洋音響; 境界値逆問題; 移流項; 再生核; 心電図; 弾性波の散乱; Carleman estimate; layer stripping method

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

本论文的主要目的是从理论和数值两方面研究反边值问题以及与之密切相关的反散射问题的唯一性、稳定性和重构性。此外，试图建立一个科学合作网络的研究人员谁在反问题在日本是另一个目的。取得了以下结果：（1）心电图的理论和数值研究。(2)探针法识别各向异性弹性介质中的夹杂物。(3)介质不均匀性对弹性波逆散射的唯一性。(4)建立了残余应力的剥层法。(5)Dirac方程反边值问题和反散射问题的唯一性。(6)定常热传导方程对流项识别的唯一性。(7)在边界处系数及其导数的局部重构 ...更多信息 他把狄利克雷映射到诺依曼映射。(8)声波逆散射问题中障碍物及其阻抗的重建。(9)利用点源重建海洋声学的折射率。(10)用切片法重建包裹体。(11)从解的值及其在与时间轴平行的超曲面上的法向导数重建初始热分布。(12)半空间中调和函数的边值由它的值及其在边界垂直的超平面上的范数重构。(13)非定常各向同性弹性方程密度判别的唯一性和稳定性。(14)在证明电导率反问题的唯一性时，弱化了电导率的正则性假设。(15)用有限测量法重建多边形空腔。(16)通过出版1998年2月举行的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一个网络。少

项目成果

M.Ikehata: "Slicing of a three-dimensional object from boundary measurements"Inverse Problems. 15. 1243-1253 (1999)

M.Ikehata：“从边界测量中切割三维物体”反问题。

M.Ikehata: "Inverse boundary value problem-----15years after Calderon raised the problem"Sugaku Expositions. 12. 57-84 (1999)

M.Ikehata：“逆边值问题-----卡尔德隆提出该问题15年后”朱乐阐述。

M. Ikehata and G. Nakamura: "Slicing of a three-dimensional object from boundary measurements"Inverse Problems. 15. 1243-1253 (1999)

M. Ikehata 和 G. Nakamura：“根据边界测量对三维物体进行切片”反问题。

M. Ikehata and G. Nakamura: "Inverse boundary value problem-15 years Calderon raised the problem"Sugaku Expositions. 12. 57-84 (1999)

M. Ikehata 和 G. Nakamura：《逆边值问题——15 年 Calderon 提出的问题》Sugaku Expositions。

G. Nakamura: "Inverse Problem and Related Topics"CRC Press LLC. 233 (2000)

G. Nakamura：“反问题及相关主题”CRC Press LLC。