2006 Fiscal Year Final Research Report Summary
Research of Optimal Control and Inverse Problems for Nonlinear Evolution Equations
| Project/Area Number |
16540194
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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 |
Global analysis
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| Research Institution | Kobe University |
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Principal Investigator |
NAKAGIRI Shin-ichi Kobe University, Faculty of Engineering, Professor, 工学部, 教授 (20031148)
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| Co-Investigator(Kenkyū-buntansha) |
TABATA Minoru Osaka Prefecture University, Faculty of Engineering, Professor, 工学部, 教授 (70207215)
NAITO Yuki Kobe University, Faculty of Engineering, Assoc. Professor, 工学部, 助教授 (10231458)
ISHII Katsuyuki Kobe University, Faculty of Maritime Sciences, Assoc. Professor, 海事科学部, 助教授 (40232227)
KOJIMA Fumio Kobe University, Graduate School of Science and Technology, professor, 自然科学研究科, 教授 (70234763)
YAGI Atsushi Osaka University, Graduate School of Technology, Professor, 大学院・工学研究科, 教授 (70116119)
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| Project Period (FY) |
2004 – 2006
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| Keywords | optimal control / inverse problem / nonlinear evolution equation / nonlinear wave / vibrating membrane / visco-elasticity / parameter identification / optimality condition |
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| Research Abstract |
According to the research plan, the head investigator Nakagiri studied and summarized the research on optimal control and inverse problems for nonlinear evolution equations. He has proved the Gateaux and Frechet differentiability of solution mappings for nonlinear first and second-order evolution equations with respect to forcing functions and initial values. Based on the results and the variational method due to Lions, we have investigated nonconvex cost optimal control problems and inverse problems for more physically important nonlinear equations such as distributed neural network equations, sine-Gordon equations, Klein-Gordon equations, viscoelastic equations, and equations of vibrating membrane with strong viscosity. These equations have own hard nonlinear structures and required the special and proper analysis of solutions. In order to solve our problems we have to obtain the delicate and proper estimates of solutions. Under the conscious of problems, we have succeeded in obtaini
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ng the results of problems for the above equations with the help of Drs Ha, Vanualailai, Hwang, and Wang. In addition, we have studied the optimal control and inverse problems for abstract nonlinear Volterra integro-differential equations with applications to viscoelastic equations with long memory. The researches of other investigators are as follows. The investigator Tabata studied the mathematical models in population movements and epidemiology. The investigator Naito studied the structure of self-similar solutions for nonlinear PDE's, and the investigator Ishii studied the convergence of algorithm for motion by mean curvature. The investigator Kojima proposed and studied the new method of data mining by the analysis of inverse problems, and applied it to the estimation problem for nondestructive testing. The investigator Yagi studied model equations appearing in mathematical physics and ecology from the stand point of infinite dimensional dynamical systems. The results of all investigators were published in the journals given below. Less
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Research Products
(128 results)
