Project/Area Number  07304017 
Research Category 
GrantinAid for Scientific Research (A)

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

Research Institution  University of Tokyo 
Principal Investigator 
MIURA Masayasu Graduate School of Mathematical Sciences, University of Tokyo, Professor, 大学院・数理科学研究科, 教授 (50068128)

CoInvestigator(Kenkyūbuntansha) 
森 正武 東京大学, 工学部, 教授 (20010936)
田端 正久 広島大学, 理学部, 教授 (30093272)
NISHIURA Yasumasa Institute of Electrical Sciences, Hokkaido University, Professor, 電子科学研究所, 教授 (00131277)
西田 孝明 京都大学, 理学部, 教授 (70026110)
岡本 久 京都大学, 数理解析研究所, 教授 (40143359)
MIYOSHI Tetsuhiko Faculty of Sciences, Yamaguchi University, Professor, 理学部, 教授 (60040101)
FUJII Hiroshi Faculty of Engineering, Kyoto, Sangyo University, Professor, 工学部, 教授 (90065839)
KAWARADA Hideo Faculty of Engineering, Chiba, University, Professor, 工学部, 教授 (90010793)
IKEDA Tsutomu Faculty of Applied Mathematics and Informatics, Ryukoku University, Professor, 理工学部, 教授 (50151296)

Project Fiscal Year 
1995 – 1996

Project Status 
Completed(Fiscal Year 1996)

Budget Amount *help 
¥6,100,000 (Direct Cost : ¥6,100,000)
Fiscal Year 1996 : ¥2,700,000 (Direct Cost : ¥2,700,000)
Fiscal Year 1995 : ¥3,400,000 (Direct Cost : ¥3,400,000)

Keywords  Bifurcation theory of flow problems / Algorithm of parallel computing / Theooretical study of domain decomposition methods / Computer aided analysis / Methods to mathematical sciences / 流体問題の分岐理論 / 並列計算アルゴリズム / 領域分割法の理論的研究 / 計算機支援解析 / 数理科学的方法論 / 数理科学的概論 / Industrial Mathematics / 数理ファイナンス / ソフトサイエンス 
Research Abstract 
Towards new development in mathematical sciences, we have considered mathematical understanding of several topics in engineering, natual sciences etc. For instance, Tabata and Okamoto have studied bifurcation theories, numerical algorithm, application to several concrete problems, parallel computing in large scale systems in fluid dynamics problems. Ikeda and Nishiura have analycally and complementarily numerically nvestigated to reveal the mecanism of phase seperation and interfacial problems in physical science, by using reactiondiffuison model systems. Mori, Kawarada and Mitsui have discussed mathemathematical topics arising in Industrial mathematics. Especially, they have developed new numerical algorithm of domain decomposition methods, which is known as one of effective scientific numerical methods. Nishida, Nakao and Tsutsumi have studied qualitative properites of nonlinear partial differential equations, from the numerical aided analysis standing point, and proposed a new analytical methods to understand nonlinear phenomena. Mimura and his group have discussed biological problems, especially aggregation, segregation of biological individuals described by reactiondiffusion systems, by integrating analytical methods, numerical simulations and visualization. This appraoch is a trial to develop new methods in mathematical sciences. The results obtained above were reperented in the meeting of Applied Mathematics in Japan which was held on December everyyear and published in the forms of proceedings. 以上の結果は、いくつかの分野での研究会そして、12月に行われた応用数学研究集会で発表され、出版物となって刊行れている。
