Mathematical analyses on variable stable structures of nonlinear free-boundaries governed by structural phase transitions

2020 Fiscal Year Final Research Report

• Project/Area Number: 16K05224
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Mathematical analysis
• Research Institution: Chiba University
• Principal Investigator: Shirakawa Ken 千葉大学, 教育学部, 准教授 (50349809)
• Project Period (FY): 2016-04-01 – 2021-03-31
• Keywords: 構造相転移 / 自由境界 / 安定構造 / 形態変化 / 抽象数学の手法 / 非線形解析学 / 幾何学的手法 / 有界変動函数の理論

Outline of Final Research Achievements

The aim of this research is to study on the variable stable structures of nonlinear free-boundaries governed by structural phase transitions. To this end, the research program consists of: the qualitative observation by means of the abstract theory of nonlinear analysis; and the geometric observation based on the theory of function of bounded variation. The principal results are concerned with: (A) mathematical modelling and analysis; (B) geometric observation of variable stable structure; (C) optimal control problem; (D) numerical analysis; and the results are published in forms of: 15 peer-reviewed papers (including 6 international collaborations); and 44 presentations (including 6 invited talks, and 13 talks in international conferences).

Free Research Field

非線形解析学

Academic Significance and Societal Importance of the Research Achievements

構造相転移は「金属の結晶」や「コロイドのベシクル」などを扱う材料科学の分野において、予測や制御が困難な現象として注目される代表的な研究テーマの一つである。この点において、本研究で実施した「自由境界の数学解析」と「最適制御問題」は、現象の予測と制御に直結した活動であり、得られた成果は「独自の数学理論の構築」という学術的意義と、「科学技術への応用の可能性に富んだ成果の産出」という社会的意義の双方の側面を併せ持っている。