Parabolic concavity of solutions of parabolic equations

2015 Fiscal Year Final Research Report

• Project/Area Number: 25610023
• Research Category: Grant-in-Aid for Challenging Exploratory Research
• Allocation Type: Multi-year Fund
• Research Field: Mathematical analysis
• Research Institution: Tohoku University
• Principal Investigator: Ishige Kazuhiro 東北大学, 理学(系)研究科(研究院), 教授 (90272020)
• Project Period (FY): 2013-04-01 – 2016-03-31
• Keywords: 放物型方程式 / 冪凸 / 放物型凸

Outline of Final Research Achievements

We introduced a new method for the study of parabolic concavity properties of solutions to parabolic boundary value problems and proved that a solutions of a nonlinear parabolic equation has parabolic power concavity properties. Furthermore, applying the arguments to parabolic concavity properties, we obtained parabolic power concavities of solutions to nonlinear parabolic systems and the relationship among the Minkowski additions of domains and the solutions of parabolic boundary value problems.

Free Research Field

偏微分方程式論