Project/Area Number  09640294 
Research Category 
GrantinAid for Scientific Research (C).

Section  一般 
Research Field 
General mathematics (including Probability theory/Statistical mathematics)

Research Institution  Nihon University 
Principal Investigator 
NAKAMURA Masaaki Nihon University, College of Science and Technology, Associate Professor, 理工学部, 助教授 (00017419)

CoInvestigator(Kenkyūbuntansha) 
HANADA Tokao Chiba Institute of Technology, Faculty of Technology, Associate Professor, 工学部, 助教授 (40017447)
SHIMA Chikayoshi Nihon University, College of Science and Technology, Associate Professor, 理工学部, 助教授 (70059674)
TAKEZAWA Terashi Nihon University, College of Science and Technology, Professor, 理工学部, 教授 (50059622)

Project Fiscal Year 
1997 – 1999

Project Status 
Completed(Fiscal Year 1999)

Budget Amount *help 
¥2,900,000 (Direct Cost : ¥2,900,000)
Fiscal Year 1999 : ¥800,000 (Direct Cost : ¥800,000)
Fiscal Year 1998 : ¥700,000 (Direct Cost : ¥700,000)
Fiscal Year 1997 : ¥1,400,000 (Direct Cost : ¥1,400,000)

Keywords  MHD system / EOM system / PVM / phase separation / Lindley process / third order equation / unbounded solution / stability / MHD系 / 複雑系 / 相分離 / 江口・沖・松村方程式 / 非線形発展系 / 高精度 / 江口・沖・松村系 / simulation / 無限精度 / Phase sepatation / attractor / spinodal decomposition / Magnetohydrodynamic eq / fractal dimension / spectral collocation method 
Research Abstract 
In the term of the project (three years) many results are obtained. Important results are shown as follows. 1. Uniqueness of the unbounded classical solution of the MHD system. We obtain the uniqueness of the unbounded classical solution of the MHD system under suitable conditions on asymptotic behaviors, MHD system is the basis of the magnetic Benard problem which we have been studying in these years. 2. Mathematical and numerical analysis of EguchiOkiMatsumura system. We introduced the mathematical formulation of the EOM system and show the existence results. We made the numerical simulation of the one dimmensional system and obtained the stability of the constant solutions. 3. Analysis of the third order equation. We obtain the nonexistence of the monotone solution of the third order equation arising in the phenomena of the liquid crysta, which has the close relation to KuramotoShivashinsky equation. 4. Analysis of the complex system in the social science. (a) We analyzed the reversibility of the Lindley process with discrete states. (b) We determined the optimal interarrival times for the queuing system GI/GI/M/1. 5. Development of the fast numerical computation and its application. We developed methods of fast numerical computations in the environment of the parallel computing offered by PVM. These methods enables the largescaled numerical simulation of fluid mechanics. 6. We held the international symposiums and domestic symposiums, for example, Fourth JapanChine joint seminar on numerical mathematics, DDM12 and RIMS symposiums. We joined the several international symposiums and presented our results.
