非線形偏微分方程式の最適制御と逆問題解析の研究

2001 年度 実績報告書

• 研究課題/領域番号: 13640213
• 研究機関: 神戸大学
• 研究代表者: 中桐 信一 神戸大学, 工学部, 教授 (20031148)
• 研究分担者: 内藤 雄基 神戸大学, 工学部, 助教授 (10231458) ; 田畑 稔 神戸大学, 工学部, 助教授 (70207215) ; 南部 隆夫 神戸大学, 工学部, 教授 (40156013) ; 小島 史夫 神戸大学, 自然科学研究科, 教授 (70234763) ; 宮川 鉄郎 神戸大学, 理学部, 教授 (10033929)
• キーワード: 最適制御 / 逆問題 / 非線形分布系 / 数理経済学 / 可安定性 / 有限要素法 / 同定問題 / 最小2乗法

研究概要

本年度の研究計画に従い、中桐は南部、田畑、内藤、宮川、小島と協力して、放物型および双曲型非線形偏微分方程式により記述される系の理論的及び数値解析的研究と、それに関する最適制御問題、逆問題、安定化問題、構造欠陥同定問題等の研究を行った。
1.中桐は、非線形双曲型方程式系に対する理論的研究およびその最適制御問題と同定問題の研究を行なった。特に減衰項を持つsine-Gordon方程式やKlein-Gordon方程式およびそのcoupled typesに対する最適制御問題とパラメータ同定の問題を研究し、コストが2次であり境界制御を含む場合に最適性の条件を与えた。
2.中桐は、神経網のHopfield型方程式に関する安定性論と最適制御問題を研究し、Practical安定性のための条件を導き、また関連する制御系の最適性の条件と最適解の存在性を示した。またその数値解析を実行した。
3.南部は放物形分布系に対する安定化の代数的方法を導入し、安定化の達成に成功した。また中桐は、遅れを含む放物形分布系に対しスペクトル論を駆使して、安定化と極配置の問題を解決した。
4.田畑は、経済地理学における非線形偏微分積分方程式により表現される非線形経済モデルの漸近挙動を、関数解析的手法を使って解析した。またその数値解析結果の数理経済学的意味を調べた。
5.内藤は半線形楕円型方程式の振動現象と正値解の構造を研究した。
6.宮川は全空間と半空間において非圧縮粘性流体の運動方程式の解の時空漸近形を考察し、空間無限遠方での挙動にある拘束条件を課した場合に、解がガウス型関数を用いて漸近展開できることを示した。
7.小島は、構造物の欠陥同定の数値解析的手法の研究を行なった。熱伝導体や弾性体の欠陥部分、空洞、亀裂等を推定するための効果的な手法の開発がなされた。

研究成果

• [文献書誌] S.Nakagiri: "Finite pole assignment of retarded dynamical systems in Hilbert spaces"Fields Institute Communications. 29. 307-320 (2001)
• [文献書誌] S.Nakagiri: "Coupled sine-Gordon equations as nonlinear second order evolution equations"Taiwanese J.Math.. 5. 297-315 (2001)
• [文献書誌] Q-F.Wang: "Weak solutions of nonlinear parabolic evolution problems with uniform Lipschitz continuous nonlinearities"Mem.Grad.School Sci.& Technol., Kobe Univ.. 19-A. 83-96 (2001)
• [文献書誌] S.Nakagiri: "Feedback stabilization of linear retarded systems in Banach spaces"J.M.A.A.. 262. 160-178 (2001)
• [文献書誌] S.Nakagiri: "Optimal control problems for damped Klein-Gordon equations"Nonlinear Analysis, Theory, Method and Applications. 47-1. 89-100 (2001)
• [文献書誌] J-H Ha: "Damped sine-Gordon equations with non-homogeneous Dirichlet boundary conditions"J.M.A.A.. 263. 708-720 (2001)
• [文献書誌] J-H Ha: "Identification problems of damped sine-Gordon equations with constant parameters"J.Korean Math. Soc. 2002.
• [文献書誌] Q-F.Wang: "Optimal control problems for distributed Hopfield-type neural networks"Nonlinear Functional Analysis and Applications. 6. (2002)
• [文献書誌] J.Vanualailai: "Convergence of Solutions and practical stability of Hopfield-type neural networks with time-varying external inputs"Nonlinear Studies. (2002)
• [文献書誌] T.Nambu: "An algebraic method of stabilization for a class of boundary control systems of parabolic Type"J.Dynamics and Differential Equations. 13-1. 59-85 (2001)
• [文献書誌] T.Nambu: "An algebraic approach to boundary stabilization for parabolic systems with Dirichlet boundaries"2nd International Workshop on Robot Motion and Control. (Proceedings). 161-167 (2001)
• [文献書誌] T.Nambu: "Output stabilization of a class of linear parabolic distributed systems"SICE Trans.. 38-2. 150-156 (2002)
• [文献書誌] T.Nambu: "Enhancement of stability of linear parabolic systems by static feedback"Applied Math. Letters. (2002)
• [文献書誌] T.Nambu: "Enhancement of stability of linear parabolic systems by static feedback"Proc.Roy.Soc.Edinburgh. (2002)
• [文献書誌] N.Eshima: "Self-organization of a stochastic agent-based model that consists of firms seeking higher desirability in business expressed by the market potential"IEEE Computer Society Press. (Proceedings). 4-8 (2001)
• [文献書誌] N.Eshima: "Analysis of the infection system of human T-cell leukemia virus type 1 based on a mathematical epidemic model"Statistics in Medicine. 20. 3891-3900 (2001)
• [文献書誌] N.Eshima: "Path analysis with logistic regression models : Effect analysis of fully recursive causal system of categorical variables"J.Japan Statist.Soc.. 31. 1-14 (2001)
• [文献書誌] M.Tabata: "A functional-analytic and numerical-analytic approach to nonlinear economic models described by the master equation"Empirical Science of Financial Fluctuations. Book. 304-311 (2002)
• [文献書誌] M.Tabata: "An infinite continuous model which derives from a finite discrete model describing the time evolution of the density of firms"Applied Mathematics and Computation. 112. 79-98 (2002)
• [文献書誌] M.Tabata: "Blowing up solutions to the Cauchy problem for the master equation"Applied Mathematics and Computation. 127. 181-193 (2002)
• [文献書誌] Y.Naito: "Oscillation criteria for quasilinear elliptic equations"Nonlinear Analysis, Theory, Method and Applications. 46-5. 629-652 (2001)
• [文献書誌] Y.Naito: "Symmetry results for semilinear elliptic equations in R^2"Nonlinear Analysis, Theory, Method and Applications. 47-6. 3661-3670 (2001)
• [文献書誌] T.Miyakawa: "On optimal decay rates for weak solutions to the Navier-Stokes equations in R^n"Mathematica Bohemica. 126. 443-455 (2001)
• [文献書誌] Y.Fujigaki: "Asymptotic profiles of nonstationary incompressible Navier-Stokes flows in the half-space"Methods and Applications of Analysis. 8. 121-158 (2001)
• [文献書誌] Y.Fujigaki: "Asymptotic profiles of nonstationary incompressible Navier-Stokes flows in the whole space"SIAM Journal on Mathematical Analysis. 33. 523-544 (2001)
• [文献書誌] Y.Fujigaki: "On solutions with fast decay of nonstationary Navier-Stokes system in the half-space"Nonlinear Problems in Mathematical Physics and Related Topics I. (2002)
• [文献書誌] T.Miyakawa: "Notes on space-time decay properties of nonstationary incompressible Navier-Stokes flows in R^n"Funkcialaj Ekvacioj. 45. (2002)
• [文献書誌] F.Kojima: "Identification of Crack Profiles using Genetic Programming and Fuzzy Inference"J.Materials Processing Technology. 108. 263-267 (2001)
• [文献書誌] N.Kubota: "Learning of Mobil Robots using Perception-based Genetic Algorithm"Measurements. 29. 237-248 (2001)
• [文献書誌] 小島史夫: "電磁非破壊評価における逆解析技術"日本AEM学会誌. 9-1. 55-65 (2001)
• [文献書誌] 小島史夫: "パラメータ推定による超伝導量子干渉計を用いた定量的非破壊評価計算法(第2報、周波数応答による深さ方向欠陥形状同定)"日本機械学会論文集(C編). 67-657. 1373-1378 (2001)
• [文献書誌] Y.Hatsukade: "Development of NDE Method Using SQUID for Reconstruction of Defect Shape"IEEE Trans.Appl.Supercond. 11. 1311-1314 (2001)
• [文献書誌] F.Kojima: "Crack profiles identification of steam generator tubes in PWR plants using database"Studies in Applied Electromagnetics and Mechanics. 21. 97-104 (2001)
• [文献書誌] F.Kojima: "Defect profiles identification of conducting materials using HTS-SQUID gradiometer with multiple frequencies"Review of Progress in Quantitative Nondestructive Evaluation. 20-A. 377-384 (2001)
• [文献書誌] F.Kojima: "Identification of materials integrity using superconducting quantum interference devices"Energy and Information in Non-Linear Systems. 20. 64-67 (2001)
• [文献書誌] N.Kubota: "Coevolutionary optimization in uncertain environments"Energy and Information in Non-Linear Systems. 20. 2-23 (2001)
• [文献書誌] F.Kojima: "Electromagnetic inverse analysis using coevolutionary algorithm and its application to crack Profiles identification"The 7th Intern.Conf.Soft Computing MENDEL, Brno, CZ. Proceedings. 74-80 (2001)
• [文献書誌] F.Kobayashi: "Knowledge sharing using belief measure in multi robot system"Knowledge-Based Inte.Info.Engi.and Applied Tech.. 69. 535-539 (2001)
• [文献書誌] Y.Nojima: "Perception and behavior of pet robots based on emotional model"Knowledge-Based Inte.Info.Engi.and Applied Tech.. 69. 859-863 (2001)
• [文献書誌] S.Hashimoto: "Genetic programming for the behavior acquisition of the perception-based robotics"Knowledge-Based Inte.Info.Engi.and Applied Tech.. 69. 869-873 (2001)
• [文献書誌] F.Kojima: "Defection and characterization of flaws in CFRP by SQUID gradiometer using evolutionary computation"Review of Progress in Quanti. Nondest. Evalu.. (2002)
• [文献書誌] F.Kojima: "Shape recovery of natural crack using evolutionary programming related to eddy current testing"I.J.Applied Electromagnetics and Mechanics. (2002)
• [文献書誌] N.Okajima: "Crack shape identification of steam generator tubes by approximate output least square problems"Studies in Applied Electromagnetics and Mechanics. (2002)
• [文献書誌] F.Kojima: "Inverse problems related to electromagnetic nondestructive evaluation"Future Directions in D.P.S.; SIAM Publisher. (2002)