2003 Fiscal Year Annual Research Report

非線形偏微分方程式の最適制御と逆問題解析の研究

Research Project

Project/Area Number	13640213
Research Institution	KOBE UNIVERSITY
Principal Investigator	中桐信一神戸大学, 工学部, 教授 (20031148)
Co-Investigator(Kenkyū-buntansha)	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) 宮川哲朗金沢大学, 理学部, 教授 (10033929)
Keywords	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
Research Abstract	本年度の研究計画に従い、中桐は研究分担者及び海外の共同研究者と協力して、非線形偏微分方程式の最適制御問題、安定性論、パラメータ同定問題(逆問題)の理論的および応用解析的研究を行った。 1.中桐は、非線形双曲型方程式系に対する最適制御問題と同定問題の研究を進めた。特に結合されたsine-Gordon方程式およびKlein-Gordon方程式に現れる物理定数の同定問題を研究し、その推定解の存在と特徴づけを与えた。 2.中桐は、積分項を含む2階非線形発展方程式に対する最適制御問題の解決をはかった。適切な観測条件のもとで最適解の存在と最適性の必要条件、推定解の正当性を求めた。さらにその結果を長期の記憶を持つ粘性弾性体の境界値最適制御問題に適用した。 3.中桐は、遅れ型の関数微分方程式に関する同定問題を研究し、非自明なスカラー観測条件のもとで、解と外部入力関数の一意性のための十分条件を導いた。また、Volterra微分積分方程式の解の安定性とその性質を研究した。 4.南部は、放物形境界制御系において、新しい代数的方法を提案し,第1種,第3種境界条件が混在する複雑な系の安定化を達成した。また、直接フィードバック機構におけるスペクトラム再配置問題を考察した。 5.田畑は、経済地理学において、自己言及型および非自己言及型エージェント・ベースト・モデルの2つを構築し、その違いを比較定理の形で評価した。また、人口移動理論におけるマスター方程式の解がフォッカー-プランク方程式の解に非常に近い事を証明した。 6.内藤は、初期時刻に特異性を持つ半線形熱方程式に対するCauchy問題の解の存在について考察を行った。また、2階非線形常微分方程式に対する2点境界値問題の解の多重存在性の考察を行った。 7.小島は、逆問題解析の電磁非破壊検査および知能ロボテイクスへの応用を通じて計測技術と逆解析の数値問題解析の連携に関する研究をおこなった。さらに逆解析解の存在および逆解析計算法の収束性能を明らかにした。

Research Products

(23 results)

All Other

All Publications (23 results)

[Publications] S.Nakagiri: "An identification problem for linear retarded functional differential equations"Journal of Inverse and Ill-Posed Problems. 11-3. 255-261 (2003)
[Publications] J.Vanualailai: "Stability of a system of Volterra integro-differential equations"Journal of Mathematical Analysis and Applications. 281. 602-619 (2003)
[Publications] J-H.Ha: "Identification problems for the damped Klein-Gordon equations"Journal of Mathematical Analysis and Applications. 289. 77-89 (2004)
[Publications] J-S.Hwang: "Optimal control for second order Volterra integro-differential equations in Hilbert space"Mem.Grad.School Sci.& Technol., Kobe Univ.. 22-A. 77-90 (2004)
[Publications] J-H.Ha: "Optimal control problems for nonlinear hyperbolic distributed parameter systems with damping terms"Funkcial Ekvacioj.. (未定). (2004)
[Publications] J-H.Ha: "Identification problems for systems governed by nonlinear damped second order equations"Journal of Korean Mathematical Society. (未定). (2004)
[Publications] S.Nakagiri: "Constant parameter identification problems of coupled sine-Gordon equations"American Mathematics Society Publications. (未定). (2004)
[Publications] S.Haruki: "On solvable operators which imply the general solution of a polygonal functional equation on the real plane"Aequationes Mathematicae. (未定). (2004)
[Publications] T.Nambu: "Stability enhancement of output for a class of linear parabolic systems"Proceedings of Royal Soceity of Edinburgh, Sec.A. 133A. 157-175 (2003)
[Publications] T.Nambu: "Boundary stabilization for linear parabolic systems with boundaries of the first kind"SICE Transactions. 40-1. 80-87 (2004)
[Publications] T.Nambu: "An L^2(Ω)-based algebraic approach to boundary stabilization for linear parabolic systems"Quarterly of Applied Mathematics. (未定). (2004)
[Publications] M.Tabata: "A self-referential agent-based model that consists of a large number of agents moving stochastically in a discrete bounded domain"Applied Mathematics and Computation. 143-2. 443-483 (2003)
[Publications] N.Eshima: "Population dynamics of HTLV-1 infection : a discrete time mathematical epidemic model approach"Journal of the Institute of Mathematics and its Applications. 20-1. 29-45 (2003)
[Publications] M.Tabata: "The behavior of stochastic agent-based models when the number of agents and the time variable tend to infinity, Applied Mathematics and Computation"Elsevier Science. (未定). (2004)
[Publications] M.Tabata: "The Fokker-Planck equation and the master equation in the theory of migration"IMA journal of Applied Mathematics. (未定). (2004)
[Publications] Y.Naito: "On the existence of multiple solutions of the boundary value problem for nonlinear second-order differential equations"Nonlinear Analysis.TMA. 56. 919-931 (2004)
[Publications] Y.Naito: "Non-uniqueness of solutions to the Cauchy problem for semilinear heat equations with singular initial data"Mathematische Annalen. (未定). (2004)
[Publications] H, Cheng: "On L^1-summability and asymptotic profiles for smooth solutions to Navier-Stokes equations in a 3D exterior domain"Mathematische Zeitschrift. 245. 387-417 (2003)
[Publications] F.Kojima: "Defect shape recovering by parameter estimation arising in eddy current testing"Journal of Korean Soceity for Nondestructive Testing. 23-6. 622-634 (2003)
[Publications] N.Kubota: "Fuzzy and Neural Computing for Communication of a Partner Robot"Journal of Multi-Valued Logic and Soft Computing. 9-2. 221-239 (2003)
[Publications] 小林太: "ベイズ推定を用いた自律搬送システム"システム制御情報学会論文誌. 16-10. 500-506 (2003)
[Publications] F.Kojima: "Reconstruction of magnetic charge densities using regularization of bounded variations under noisy observations"International journal of Applied Electromagnetics and Mechanics. (未定). (2004)
[Publications] H.T.Banks, F.Kojima et al.Edi.: "Inverse Problems related to Electromagnetic Nondestructive Evaluation, SIAM Frontiers in Applied Mathematics, Vol.FR27, pp.219-236"SIAM Publications. 290 (2003)

2003 Fiscal Year Annual Research Report

非線形偏微分方程式の最適制御と逆問題解析の研究

Principal Investigator

中桐 信一 神戸大学, 工学部, 教授 (20031148)

Research Products

[Publications] S.Nakagiri: "An identification problem for linear retarded functional differential equations"Journal of Inverse and Ill-Posed Problems. 11-3. 255-261 (2003)

[Publications] J.Vanualailai: "Stability of a system of Volterra integro-differential equations"Journal of Mathematical Analysis and Applications. 281. 602-619 (2003)

[Publications] J-H.Ha: "Identification problems for the damped Klein-Gordon equations"Journal of Mathematical Analysis and Applications. 289. 77-89 (2004)

[Publications] J-S.Hwang: "Optimal control for second order Volterra integro-differential equations in Hilbert space"Mem.Grad.School Sci.& Technol., Kobe Univ.. 22-A. 77-90 (2004)

[Publications] J-H.Ha: "Optimal control problems for nonlinear hyperbolic distributed parameter systems with damping terms"Funkcial Ekvacioj.. (未定). (2004)

[Publications] J-H.Ha: "Identification problems for systems governed by nonlinear damped second order equations"Journal of Korean Mathematical Society. (未定). (2004)

[Publications] S.Nakagiri: "Constant parameter identification problems of coupled sine-Gordon equations"American Mathematics Society Publications. (未定). (2004)

[Publications] S.Haruki: "On solvable operators which imply the general solution of a polygonal functional equation on the real plane"Aequationes Mathematicae. (未定). (2004)

[Publications] T.Nambu: "Stability enhancement of output for a class of linear parabolic systems"Proceedings of Royal Soceity of Edinburgh, Sec.A. 133A. 157-175 (2003)

[Publications] T.Nambu: "Boundary stabilization for linear parabolic systems with boundaries of the first kind"SICE Transactions. 40-1. 80-87 (2004)

[Publications] T.Nambu: "An L^2(Ω)-based algebraic approach to boundary stabilization for linear parabolic systems"Quarterly of Applied Mathematics. (未定). (2004)

[Publications] M.Tabata: "A self-referential agent-based model that consists of a large number of agents moving stochastically in a discrete bounded domain"Applied Mathematics and Computation. 143-2. 443-483 (2003)

[Publications] N.Eshima: "Population dynamics of HTLV-1 infection : a discrete time mathematical epidemic model approach"Journal of the Institute of Mathematics and its Applications. 20-1. 29-45 (2003)

[Publications] M.Tabata: "The behavior of stochastic agent-based models when the number of agents and the time variable tend to infinity, Applied Mathematics and Computation"Elsevier Science. (未定). (2004)

[Publications] M.Tabata: "The Fokker-Planck equation and the master equation in the theory of migration"IMA journal of Applied Mathematics. (未定). (2004)

[Publications] Y.Naito: "On the existence of multiple solutions of the boundary value problem for nonlinear second-order differential equations"Nonlinear Analysis.TMA. 56. 919-931 (2004)

[Publications] Y.Naito: "Non-uniqueness of solutions to the Cauchy problem for semilinear heat equations with singular initial data"Mathematische Annalen. (未定). (2004)

[Publications] H, Cheng: "On L^1-summability and asymptotic profiles for smooth solutions to Navier-Stokes equations in a 3D exterior domain"Mathematische Zeitschrift. 245. 387-417 (2003)

[Publications] F.Kojima: "Defect shape recovering by parameter estimation arising in eddy current testing"Journal of Korean Soceity for Nondestructive Testing. 23-6. 622-634 (2003)

[Publications] N.Kubota: "Fuzzy and Neural Computing for Communication of a Partner Robot"Journal of Multi-Valued Logic and Soft Computing. 9-2. 221-239 (2003)

[Publications] 小林 太: "ベイズ推定を用いた自律搬送システム"システム制御情報学会論文誌. 16-10. 500-506 (2003)

[Publications] F.Kojima: "Reconstruction of magnetic charge densities using regularization of bounded variations under noisy observations"International journal of Applied Electromagnetics and Mechanics. (未定). (2004)

[Publications] H.T.Banks, F.Kojima et al.Edi.: "Inverse Problems related to Electromagnetic Nondestructive Evaluation, SIAM Frontiers in Applied Mathematics, Vol.FR27, pp.219-236"SIAM Publications. 290 (2003)

中桐信一神戸大学, 工学部, 教授 (20031148)

[Publications] 小林太: "ベイズ推定を用いた自律搬送システム"システム制御情報学会論文誌. 16-10. 500-506 (2003)