2000 Fiscal Year Annual Research Report

非線形放物型および双曲型分布定数系の制御理論と同定問題の理論および数値解析的研究

Research Project

Project/Area Number	11640201
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)
Keywords	最適制御 / 同定問題 / 非線形分布系 / 可同定性 / 可安定性 / 有限要素法 / 半群理論 / 最小2乗法
Research Abstract	本年度の研究計画に従い、中桐は南部、田畑、内藤と協力して、1階および2階の非線形偏微分方程式により記述される系の理論的研究と、それに関する最適制御問題とパラメータ同定問題の研究を継続して行った。 1.非有界な非線型性の仮定のもとで、Wangとの協力により、中桐は1階の時変発展方程式で記述される系の解の存在と一意性および正則性の結果を導いた。加えて、関連する最適制御問題の解の構成と最適性の条件を導いた。またその数値解析を研究した。 2.分布系が、分布型Hopfield-typeニューラルネットワーク方程式で記述される場合に最適制御問題を研究し、中桐、Wang及びJito Vanualailaiは、解の安定性、最適解の存在を示し、最適性の条件を求めた。また、時間遅れのある1階の発展方程式系に対し、中桐は極配置可能性と可安定性の為の必要かつ十分条件を求めた。 3.減衰項をもつ非線形双曲型分布系の未知パラメータの同定問題を研究した。Haの協力を得て、中桐は一般的な観測のもとてのパラメータ同定性の必要条件を求めた。 4.分布系が減衰項を持つcoupled sine-Gordon方程式である場合に、最適制御問題と、方程式に含まれる物理パラメータの同定問題を研究した。中桐は、Haと共にこれらの問題に対し、最適解の存在、最適性の必要条件および、パラメータ同定のための必要条件を導いた。 5.分布系が非線型Klein-Gordon方程式である場合に、上と同様の問題を研究した。理論的な部分は、中桐、Haによりほぼ解決された。 6.上記の研究に加え、南部は安定化の代数的方法を、田畑は経済地理学における数理モデルを、内藤は半線形楕円型方程式の正値解の構造を研究した。

Research Products
(21 results)

All Other

All Publications (21 results)

[Publications] Q-F.Wang: "Optimal Control Problems for Parabolic Distributed Parameter Systems with Uniform Lipschitz Continuous Nonlinearities"Mem.Grad.School Sci.& Technol., Kobe Univ.. 18-A. 113-129 (2000)
[Publications] S.Nakagiri: "Quadratic cost optimal control problems for damped Klein-Gordon equations"Proc.RESCCE'2000 JAPAN-USA-VIETNAM Workshop. 261-270 (2000)
[Publications] S.Nakagiri: "Finite pole assignment of retarded dynamical systems in Hilbert spaces"Fields Institute Communications. 22. (2001)
[Publications] S.Nakagiri: "Coupled sine-Gordon equations as nonlinear second order evolution equations"Taiwanese J.Math.. (2001)
[Publications] S.Nakagiri: "Feedback stabilization of linear retarded systems in Banach spaces"J.M.A.A.. (2001)
[Publications] S.Nakagiri: "Optimal control problems for damped Klein-Gordon equations"Nonlinear Analysis, Theory, Method and Applications. (2001)
[Publications] J-H Ha: "Optimal control problems for nonlinear hyperbolic distributed parameter systems with damping terms"Funkcial.Ekvac.. (2001)
[Publications] J-H Ha: "Identification problems for systems governed by nonlinear damped second order equations"Nonlinear Analysis, Theory, Method and Applications. (2001)
[Publications] Q-F.Wang: "Weak solutions of nonlinear parabolic evolution problems with uniform Lipschitz continuous nonlinearities"Mem.Grad.School Sci.& Technol., Kobe Univ.. 19-A. (2001)
[Publications] 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)
[Publications] M.Tabata: "The behaviour of solution to the Cauchy problem for the master equation"Applied Mathematics and Computation. 112. 79-98 (2000)
[Publications] M.Tabata: "The point spectrum of the linearized Boltzmann operator with an external potential in an unbounded domain"Taiwanese J.Math.. 4-2. 297-306 (2000)
[Publications] M.Tabata: "Decay of solutions to the mixed problem for the linearized Boltzmann equation with a potential term in a polyhedral bounded domain"Rendiconti dell Sem.Mat.Univ.Padova. 103-1. 1-23 (2000)
[Publications] 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. (2001)
[Publications] M.Tabata: "Blowing up solutions to the Cauchy problem for the master equation"Applied Mathematics and Computation. (2001)
[Publications] N.Eshima: "Property of the RC (M) association model and a correlation coefficient in the contigency table"Journal of the Japan Statistical Society. 31-1. 109-120 (2001)
[Publications] Y.Naito: "Radial symmetry of self-similar solutions for semilinear elliptic equalions"J.Differential Equations. 215-234 (2000)
[Publications] Y.Naito: "Non existence results of positive solutions for for semilinear elliptic equalions in R^2"J.Math.Soc.Japan. (2000)
[Publications] Y.Naito: "Radial symmetry of positive solutions for semilinear elliptic equations in R^n"J.Korean Math.Soc.. 37. 751-761 (2000)
[Publications] N.Muramoto: "Existence of self-similar solutions to a parabolic system modelling chemotaxis"Japan J.Indust.Appl.Math.. 17. 427-451 (2000)
[Publications] 南部隆夫: "微分方程式入門"朝倉書店. 245 (2000)

2000 Fiscal Year Annual Research Report

非線形放物型および双曲型分布定数系の制御理論と同定問題の理論および数値解析的研究

Principal Investigator

中桐 信一 神戸大学, 工学部, 教授 (20031148)

Research Products

[Publications] Q-F.Wang: "Optimal Control Problems for Parabolic Distributed Parameter Systems with Uniform Lipschitz Continuous Nonlinearities"Mem.Grad.School Sci.& Technol., Kobe Univ.. 18-A. 113-129 (2000)

[Publications] S.Nakagiri: "Quadratic cost optimal control problems for damped Klein-Gordon equations"Proc.RESCCE'2000 JAPAN-USA-VIETNAM Workshop. 261-270 (2000)

[Publications] S.Nakagiri: "Finite pole assignment of retarded dynamical systems in Hilbert spaces"Fields Institute Communications. 22. (2001)

[Publications] S.Nakagiri: "Coupled sine-Gordon equations as nonlinear second order evolution equations"Taiwanese J.Math.. (2001)

[Publications] S.Nakagiri: "Feedback stabilization of linear retarded systems in Banach spaces"J.M.A.A.. (2001)

[Publications] S.Nakagiri: "Optimal control problems for damped Klein-Gordon equations"Nonlinear Analysis, Theory, Method and Applications. (2001)

[Publications] J-H Ha: "Optimal control problems for nonlinear hyperbolic distributed parameter systems with damping terms"Funkcial.Ekvac.. (2001)

[Publications] J-H Ha: "Identification problems for systems governed by nonlinear damped second order equations"Nonlinear Analysis, Theory, Method and Applications. (2001)

[Publications] Q-F.Wang: "Weak solutions of nonlinear parabolic evolution problems with uniform Lipschitz continuous nonlinearities"Mem.Grad.School Sci.& Technol., Kobe Univ.. 19-A. (2001)

[Publications] 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)

[Publications] M.Tabata: "The behaviour of solution to the Cauchy problem for the master equation"Applied Mathematics and Computation. 112. 79-98 (2000)

[Publications] M.Tabata: "The point spectrum of the linearized Boltzmann operator with an external potential in an unbounded domain"Taiwanese J.Math.. 4-2. 297-306 (2000)

[Publications] M.Tabata: "Decay of solutions to the mixed problem for the linearized Boltzmann equation with a potential term in a polyhedral bounded domain"Rendiconti dell Sem.Mat.Univ.Padova. 103-1. 1-23 (2000)

[Publications] 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. (2001)

[Publications] M.Tabata: "Blowing up solutions to the Cauchy problem for the master equation"Applied Mathematics and Computation. (2001)

[Publications] N.Eshima: "Property of the RC (M) association model and a correlation coefficient in the contigency table"Journal of the Japan Statistical Society. 31-1. 109-120 (2001)

[Publications] Y.Naito: "Radial symmetry of self-similar solutions for semilinear elliptic equalions"J.Differential Equations. 215-234 (2000)

[Publications] Y.Naito: "Non existence results of positive solutions for for semilinear elliptic equalions in R^2"J.Math.Soc.Japan. (2000)

[Publications] Y.Naito: "Radial symmetry of positive solutions for semilinear elliptic equations in R^n"J.Korean Math.Soc.. 37. 751-761 (2000)

[Publications] N.Muramoto: "Existence of self-similar solutions to a parabolic system modelling chemotaxis"Japan J.Indust.Appl.Math.. 17. 427-451 (2000)

[Publications] 南部隆夫: "微分方程式入門"朝倉書店. 245 (2000)

中桐信一神戸大学, 工学部, 教授 (20031148)