Singularity of solutions for nonlinear partial differential equations of parabolic type and structure of solutions for the stationary problems

2014 Fiscal Year Final Research Report

• Project/Area Number: 23540244
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Global analysis
• Research Institution: Ehime University
• Principal Investigator: NAITO Yuki 愛媛大学, 理工学研究科, 教授 (10231458)
• Co-Investigator(Kenkyū-buntansha): KAJIKIYA Ryuji 佐賀大学, 大学院工学研究科, 教授 (10183261) ; ISHII Katsuyuki 神戸大学, 大学院海事科学研究科, 教授 (40232227)
• Co-Investigator(Renkei-kenkyūsha): YANAGIDA Eiji 東京工業大学, 大学院理工学研究科, 教授 (80174548) ; SENBA Takasi 九州工業大学, 大学院工学研究科, 教授 (30196985) ; YOSHIKAWA Syuji 愛媛大学, 大学院理工学研究科, 准教授 (80435461) ; IOKU Norisuke 愛媛大学, 大学院理工学研究科, 助教 (50624607)
• Project Period (FY): 2011-04-28 – 2015-03-31
• Keywords: 放物型偏微分方程式 / 定常問題 / 非線形解析 / 自己相似解 / 解の爆発

Outline of Final Research Achievements

We study the singular behavior of solutions for nonlinear partial differential equations of parabolic type, and investigate the relations between the singularity and the solution structure of the stationary problems. We verify the roles of self-similar solutions in the Cauchy problems for semilinear heat equations in the case where the problem has multiple self-similar solutions. We consider the Cauchy problem for semilinear heat equations, and show the optimal spatial decay condition of initial functions at infinity for the blow-up in finite time. We consider the elliptic partial differential equations involving p-Laplace
operator, and show the geometrical properties of radially symmetric solutions which has singular behavior near the boundary.

Free Research Field

数物系科学