MATHEMATICAL ANALYSIS FOR INVERSE PROBLEMS IN CONTINUUM MECHANICS
Grant-in-Aid for Scientific Research (C)
|Allocation Type||Single-year Grants |
|Research Institution||Gunma University |
NAKAMURA Gen GUNMA UNIV. COMMON, PROFESSOR, 工学部, 教授 (50118535)
ONISHI Kazuei IBARAKI UNIV. MATH. SCI., PROFESSOR, 理学部, 教授 (20078554)
IKEHATA Masaru GUNMA UNIV. COMMON, ASSIST. PROFESSOR, 工学部, 助教授 (90202910)
SAITOH Saburoh GUNMA UNIV. COMMON, PROFESSOR, 工学部, 教授 (10110397)
TSUCHIDA Tetsuo KIYUSHU UNIV. GRAD. SCH., ASSISTANT, 大学院・数理学研究科, 助手 (10274432)
TANUMA Kazumi OSAKA KYOIKU UNIV. EDUCATION, ASSIST. PROFESSOR, 教育学部, 助教授 (60217156)
山本 昌宏 東京大学, 大学院・数理科学研究科, 助教授 (50182647)
川下 美潮 茨城大学, 教育学部, 助教授 (80214633)
|Project Period (FY)
1998 – 1999
Completed (Fiscal Year 1999)
|Budget Amount *help
¥1,700,000 (Direct Cost: ¥1,700,000)
Fiscal Year 1999: ¥700,000 (Direct Cost: ¥700,000)
Fiscal Year 1998: ¥1,000,000 (Direct Cost: ¥1,000,000)
|Keywords||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
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
Report (3 results)
Research Products (33 results)