Mathematics of reconstruction of the surface of discontinuity inside a body from observation data

根据观测数据重建体内不连续表面的数学

• 批准号: 11640151
• 负责人: IKEHATA Masaru
• 金额: $ 1.98万
• 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: 1999
• 资助国家: 日本
• 起止时间: 1999 至 2000
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-11640151/
• 关键词: inverse problem; Cauchy problem; inverse boundary value problem; Dirichlet; Neumann; inverse conductivity problem; the probe method; inverse scattering problem; 散乱振幅; 探針法; 散乱抓幅; Dirichlct-to-Neumann写像; 逆源泉問題; 導電率

We considered the problem of extracting several information about the coefficient in a uniformly elliptic equation in a bounded domain from the Cauchy data on the boundary of the domain of infinitely many solutions of the equation. We proposed three mathematical methods for the purpose. These are called the probe method, the enclosure method and the slice method. Applications to the Cauchy problem, the inverse scattering problem and the inverse conductivity problem in an unbounded domain are given.

我们考虑了从无限多个方程域的边界上的cauchy数据中提取有关椭圆形域中均匀椭圆方程中系数的几个信息的问题。我们为此目的提出了三种数学方法。这些称为探针方法，外壳方法和切片方法。给出了无界域中的库奇问题，反向散射问题和反导率问题的应用。

项目成果

Ikehata,M.: "Reconstruction of the support function for inclusion from boundary measurements"J Inv.and Ill-Posed Problcms. vol.8(印刷中). (2000)

Ikehata, M.：“从边界测量中重建支持函数”J Inv. 和不适定问题第 8 卷（出版中）。

Ikehata,M: "The enclosure method and its applications"Analytic extension formulas and its applications. (in press).

Ikehata，M：“包围法及其应用”解析扩展公式及其应用。

Ikehata,M: "Exponentially growing solutions and the Cauchy problem."Applicable Analysis. (in press).

Ikehata,M：“指数增长的解决方案和柯西问题。”适用分析。

Ikehata,M and Nakamura.G: "Inverse boundary value problem…, 15y years since Calder'on raised Problem."Sugaku Expositions.. 12. 57-84 (1999)

Ikehata,M 和 Nakamura.G：“逆边值问题……，自 Calderon 提出问题以来 15 年。”Sugaku Expositions.. 12. 57-84 (1999)

K.Tanuma: "Surface impedance tensor and boundary value problem"Inverse Problems and related topics, Researh Note in Mathematics 419, chapmen & Hall/CRC. 181-187 (2000)

K.Tanuma：“表面阻抗张量和边值问题”反问题及相关主题，数学研究笔记 419，chapmen