Unified investigation on elliptic and parabolic equations

2014 Fiscal Year Final Research Report

• Project/Area Number: 23540248
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Global analysis
• Research Institution: Osaka Prefecture University
• Principal Investigator: KABEYA Yoshitsugu 大阪府立大学, 工学(系)研究科(研究院), 教授 (70252757)
• Co-Investigator(Renkei-kenkyūsha): ISHIGE Kazuhiro 東北大学, 理学研究科, 教授 (90272020)
• Project Period (FY): 2011-04-28 – 2015-03-31
• Keywords: ホットスポット / 楕円型方程式 / 放物型方程式 / 時間大域挙動 / 時間減衰 / シュレディンガー半群

Outline of Final Research Achievements

With Professor Kazuhiro Ishige, who is my liaison collabolator, I investigated the large time behaviors of solutions to linear parabolic equations. During the research, I found that properties of a positive solution to the corresponding elliptic equations, which describe the steady states, affect the large time behaviors of solutions and published the main results in Journal of Functional analysis in 2012. Also related results on large time behaviors of solutions were
published in foreign academic journals.
Properties of solutions to elliptic equations on a sphere or on the hyperbolic space were also invesitgated and published in foreign academic journals.

Free Research Field

偏微分方程式論