2001 Fiscal Year Final Research Report Summary
RECONSTRUCTION PROCEDURE FOR INVERSE PROBLEMS
| Project/Area Number |
12640153
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | HOKKAIDO UNIVERSITY (2001)
Gunma University (2000) |
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Principal Investigator |
NAKAMURA Gen HOKKAIDO UNIV., GRAD. SCHOOL OF SCI., PROFESSOR, 大学院・理学研究科, 教授 (50118535)
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| Co-Investigator(Kenkyū-buntansha) |
TANUMA Kazumi GUNMA UNIV., FAC. OF ENGINEERIG, ASSIST. PROFESSOR, 工学部, 助教授 (60217156)
ONISHI Kazuei IBARAKI UNIV., FAC. OF SCIENCE., PROFESSOR, 理学部, 教授 (20078554)
IKEHATA Masaru GUMA UNIV., FAC. OF ENGINEERING, PROFESSOR, 工学部, 教授 (90202910)
KAWASHITA Mishio HIROSHIMA UNIV., GRAD. SCHOOL OF SCI., ASSIST. PROFESSOR, 大学院・理学研究科, 助教授 (80214633)
ISOZAKI Hiroshi TOKYO MET. UNIV., GRAD. SCHOOL OF SCI., PROFESSOR, 大学院・理学研究科, 教授 (90111913)
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| Project Period (FY) |
2000 – 2001
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| Keywords | INVERSE PROBLEMS / DIRICHLET TO NEUMANN MAP / UNIQUENESS / RECONSTRUCTION / DISCRETIZATION / RESIDUAL STRESS / TRANSVERSALLY ISOTROPIC / INVERSE SCATTERING / ACOUSTICAL SCATTERING / INCLUSION / PIEZOELECTRICITY / WELL POSEDNESS / CRACK / CONDUCTIVITY EQUATION / CAUCHY DATA |
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| Research Abstract |
The following results were obtained.
(1) As a preparation of the research on the inverse problem for piezoelectricity, the well posedness of the initial boundary value problem for the equation of piezoelectricity was proven.
(2) The uniqueness of identifying the coefficients of the nonlinear term of the second degree in the conductivety equation from the Dirichlet to Neumann map was proven.
(3) The identification of the residual stress depending on the depth was considered for the inverse problem associated with the Lamb problem. The reconstruction procedure at the boundary was given for the general case and that of in the interior was given for a special case.
(4) In order to apply the oscillating-decaying solution to inverse problem, the relation between the Cauchy data of the boundary value problem for anisotropic conductive equation with analytic conductivity and the singularity of its solution was shown.
(5) The asymptotic expansion of the solution for the Lame system with inclusions as their diameter tends to zero was proven.
(6) The reconstruction procedure of identifying impenetrable obstacles and their physical properties for acoustical inverse scattering problem from farfield pattern was given.
(7) A reconstruction formula for identifying the material coefficients pointwisely from the localized Dirichlet to Neumann map was given.
(8) The unique continuation for transversally isotropic elastic equation and isotropic elastic equation with residual stress were proven. Also, as their application Runge properties for these equations were proven.
(9) An approximate identification for the inverse boundary value problem for the Schrodinger equation with potential from the discretized Dirichlet to Neumann map was proven.
(10) The global uniqueness for the inverse boundary value problem for identifying the convection term of the steady state heat equation from the Dirichlet to Neuman map was proven.
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