Mathematics of inverse problems and practical solution methods

反问题数学及实用解法

• 批准号: 21340021
• 负责人: YAMAMOTO Masahiro
• 金额: $ 10.82万
• 依托单位: The University of Tokyo
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (B)
• 财政年份: 2009
• 资助国家: 日本
• 起止时间: 2009 至 2012
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-21340021/
• 关键词: 逆問題; 数値解析; 実用解法; 正則化; 安定化

We made mathematical researches for various applied inverse problems and established numerical methods which are applicable practically. As applied inverse problems, we studied inverse coefficient problems, inverse source problems, inverse obstacle scattering problem and image reconstruction, and our mathematical subjects are the uniqueness and the stability.

对各种应用反问题进行了数学研究，建立了实用的数值方法。作为应用反问题，我们研究了反系数问题、反源问题、反障碍物散射问题和图像重建问题，我们的数学主题是唯一性和稳定性。

项目成果

On the interplay of source conditions and variational inequalities for nonlinear ill-posed problems

• DOI: 10.1080/00036810903208148
• 发表时间: 2010-01-01
• 期刊: APPLICABLE ANALYSIS
• 影响因子: 1.1
• 作者: Hofmann, Bernd;Yamamoto, Masahiro
• 通讯作者: Yamamoto, Masahiro

Determination of source terms in a degenerate parabolic equation

• DOI: 10.1088/0266-5611/26/10/105003
• 发表时间: 2010-10
• 期刊: Inverse Problems
• 影响因子: 2.1
• 作者: P. Cannarsa;J. Tort;Masahiro Yamamoto

Kazumi Recovering conductivity at the boundary in three-dimensional electrical impedance tomography

Kazumi 在三维电阻抗断层扫描中恢复边界处的电导率

• 发表时间: 2011
• 期刊: Inverse Probl. Imaging 5
• 作者: Nakamura;Gen; Ronkanen;Paivi; Siltanen;Samuli; Tanuma
• 通讯作者: Samuli; Tanuma

A backward problem for the time-fractional diffusion equation

时间分数扩散方程的后向问题

• DOI: 10.1080/00036810903479731
• 发表时间: 2010-09
• 期刊: Applicable Analysis
• 影响因子: 1.1
• 作者: M.Yamamoto;J.J.Liu
• 通讯作者: J.J.Liu

Conditional stability in determining a zeroth-order coefficient in a half-order fractional diffusion equation by a Carleman estimate

• DOI: 10.1088/0266-5611/28/10/105010
• 发表时间: 2012-09
• 期刊: Inverse Problems
• 影响因子: 2.1
• 作者: Masahiro Yamamoto;Ying Zhang