Removability and asymptotic profile of dynamic singularities in parabolic partial differential equations

2015 Fiscal Year Final Research Report

• Project/Area Number: 25610026
• Research Category: Grant-in-Aid for Challenging Exploratory Research
• Allocation Type: Multi-year Fund
• Research Field: Mathematical analysis
• Research Institution: Tokyo Institute of Technology
• Principal Investigator: YANAGIDA Eiji 東京工業大学, 理工学研究科, 教授 (80174548)
• Co-Investigator(Kenkyū-buntansha): KAN Toru 東京工業大学, 大学院理工学研究科, 助教 (60647270)
• Project Period (FY): 2013-04-01 – 2016-03-31
• Keywords: 関数方程式 / 解析学 / 特異点 / 除去可能性 / 非線形

Outline of Final Research Achievements

For the heat equation, we obtained a necessary and sufficient condition for the removability of singularities, and showed the existence of solutions whose singularities vary in time. Next, for Fujita-type equations, we studied properties of radially symmetric solutions and made clear the relation between initial values and convergence rates to the stationary solutions. For a semilinear parabolic equation with absorption, we made clear conditions for the removability of dynamic singularities, and showed that when non-removable, any singular solution can be classified into two types depending on the strength of singularities.

Free Research Field

数物系科学