| Project/Area Number |
24244012
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| Research Category |
Grant-in-Aid for Scientific Research (A)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Global analysis
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| Research Institution | Tokyo Institute of Technology |
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Principal Investigator |
Yanagida Fiji 東京工業大学, 理学院, 教授 (80174548)
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| Co-Investigator(Kenkyū-buntansha) |
仙葉 隆 福岡大学, 理学部, 教授 (30196985)
内藤 雄基 愛媛大学, 理工学研究科(理学系), 教授 (10231458)
壁谷 喜継 大阪府立大学, 工学(系)研究科(研究院), 教授 (70252757)
石渡 通徳 大阪大学, 基礎工学研究科, 教授 (30350458)
高坂 良史 神戸大学, 海事科学研究科, 准教授 (00360967)
谷口 雅治 岡山大学, 自然科学研究科, 教授 (30260623)
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| Research Collaborator |
Polacik Peter University of Minnesota, School of Mathematics, Professor
Fila Marek Comenius University, Department of Applied Mathematics and Statistics, Professor
Shi Jun-Ping College of William and Mary, Mathematics, Professor
Htoo Khin Phyu Phyu Mandalay University, Department of Mathematics, Lecturer
Hui Kin-Ming Academia Sinica, Institute of Mathematics, Research Fellow(Professor)
Chern Jann-Long National Central University, Department of Mathematics, Professor
Chen Chiun-Chuan National Taiwan University, Department of Mathematics, Professor
Marta Garcia-Huidobro Pontificia Universidad Catálica de Chile, Facultad de Mathemóticas, Professor
Lou Yuan Ohio States University, Deaprtment of Mathematics, Professor
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| Project Period (FY) |
2012-05-31 – 2017-03-31
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| Project Status |
Completed (Fiscal Year 2017)
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| Budget Amount *help |
¥44,720,000 (Direct Cost: ¥34,400,000、Indirect Cost: ¥10,320,000)
Fiscal Year 2016: ¥9,490,000 (Direct Cost: ¥7,300,000、Indirect Cost: ¥2,190,000)
Fiscal Year 2015: ¥9,230,000 (Direct Cost: ¥7,100,000、Indirect Cost: ¥2,130,000)
Fiscal Year 2014: ¥8,970,000 (Direct Cost: ¥6,900,000、Indirect Cost: ¥2,070,000)
Fiscal Year 2013: ¥8,320,000 (Direct Cost: ¥6,400,000、Indirect Cost: ¥1,920,000)
Fiscal Year 2012: ¥8,710,000 (Direct Cost: ¥6,700,000、Indirect Cost: ¥2,010,000)
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| Keywords | 形状解析 / 漸近挙動 / 安定性 / 特異性 / 進行波解 / 解の爆発 / 関数方程式 / 解析学 / 楕円型方程式 / 熱方程式 / 走化性方程式 / 関数方程式の大域理論 / 分岐構造 |
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| Outline of Final Research Achievements |
We carried out systematic studies on the profile and behavior of solutions of elliptic and parabolic partial differential equations, and obtained the following results among others.
For elliptic equations, we showed a Liouville-type theorem for an equation transformed by a scaling method. We also obtained results on the existence and no-existence of singular solutions and the structure of positive solutions for equations on the sphere, and equations with space-dependent exponent of nonlinearities.
For parabolic equations, we made clear the structure of solutions of a linear heat equation with inverse-square potential. We also studied the Fujita equation about the boundedness of time-global solutions, existence of singular solutions and their stability, and Fisher's equation about the dynamics of interfaces.
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