Blowup problems for nonlinear heat equations

2017 Fiscal Year Final Research Report

• Project/Area Number: 26800065
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Mathematical analysis
• Research Institution: Akita University
• Principal Investigator: Harada Junichi 秋田大学, 教育文化学部, 准教授 (00580169)
• Project Period (FY): 2014-04-01 – 2018-03-31
• Keywords: 爆発問題 / 非線形熱方程式 / 同時・非同時爆発 / 日自己相似爆発

Outline of Final Research Achievements

We studied the mechanism of singularities for nonlinear diffusion equations. Since singularities include much information about the character of each equation, we can understand new phenomenons hidden in the equation. In this study, we focused on singularities appearing in diffusion equations for a higher dimension. We extended conventional theories and treated wide class of nonlinear problems. Consequently, we found a new type of singularity.

Free Research Field

非線形偏微分方程式