Qualitative theory of nonlinear partial differential equations and the analysis of singularitiesof

2015 Fiscal Year Final Research Report

• Project/Area Number: 23244017
• Research Category: Grant-in-Aid for Scientific Research (A)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Global analysis
• Research Institution: The University of Tokyo
• Principal Investigator: Matano Hiroshi 東京大学, 数理(科)学研究科(研究院), 教授 (40126165)
• Co-Investigator(Kenkyū-buntansha): NAKAMURA Ken-Ichi 金沢大学, 数物科学系, 准教授 (40293120) ; FUNAKI Tadahisa 東京大学, 大学院数理科学研究科, 教授 (60112174)
• Co-Investigator(Renkei-kenkyūsha): NARA Mitsunori 岩手大学, 人文社会学部, 准教授 (90512161)
• Project Period (FY): 2011-04-01 – 2016-03-31
• Keywords: 非線形偏微分方程式 / 定性的理論 / 進行波 / 界面運動 / 解の爆発 / 特異極限 / 自由境界問題

Outline of Final Research Achievements

In this research project, I made a sytematic study of the long-time behavior and stability of solutions of nonlinear partial differential equations, and also singularities arising in those solutions, by using asymptotic methods and the theory of infinite dimensional dynamical systems. More specifically, I focused on the following topics: (1) Traveling waves and spreading fronts of various kinds; (2) Qualitative study of the long-time behavior of solutions; (3) Singular limit of nonlinear diffusion equations and the associated interface motion.
These themes include free boundary problems such as the nonlinear Stefan problem.

Free Research Field

非線形解析学