Blow-up problem for a nonlinear diffusion equation and its diffusion coefficient

非线性扩散方程及其扩散系数的爆炸问题

• 批准号: 24840027
• 负责人: FUJISHIMA Yohei
• 金额: $ 1.91万
• 依托单位: Osaka University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Research Activity Start-up
• 财政年份: 2012
• 资助国家: 日本
• 起止时间: 2012-08-31 至 2014-03-31
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-24840027/
• 关键词: 非線形偏微分方程式; 爆発問題; 爆発集合; 拡散係数; 解の形状; 非線形熱方程式; 指数型非線形項; 比較原理; 優解; 劣解; Liouville型定理

This research program is devoted to the study of the relationship between the blow-up problem for a nonlinear heat equation and the diffusion coefficient. In particular, I have studied the characterization of the location of the blow-up set under a small diffusion situation.In the first year of this program, I applied the results of the blow-up problem with small diffusion, and proved the non-existence of the radially symmetric solution which blows up on the boundary for a nonlinear heat equation on an annulus.In the final year of this program, I have studied the blow-up problem for a superlinear heat equation with general nonlinearity including exponential nonlinearity. In particular, I characterized the location of the blow-up set of solutions with small diffusion.

该研究项目致力于研究非线性热方程的爆炸问题与扩散系数之间的关系。特别是，我研究了小扩散情况下爆炸集位置的表征。在这个项目的第一年，我应用了小扩散情况下爆炸问题的结果，并证明了非-环面上非线性热方程的径向对称解的存在性在边界上爆炸。在本课程的最后一年，我研究了具有一般非线性（包括指数非线性）的超线性热方程的爆炸问题。特别是，我描述了具有小扩散的爆炸组溶液的位置。

项目成果

Stability for parabolic quasiminimizers

抛物线准极小化器的稳定性

• 发表时间: 2014
• 作者: T Saito;Y Sawaki;他6名;Shouhei Ma;藤嶋陽平
• 通讯作者: 藤嶋陽平

Blow-up set for type I blowing up solutions for a semilinear heat equation

用于半线性热方程 I 型解的爆炸套件

• 发表时间: 2012
• 作者: K. Bogdan;T. Kumagai;M. Kwaśnicki;熊谷隆;熊谷隆;石毛和弘;熊谷隆;Takayuki Fujii and Masayuki Uchida;熊谷隆;Kengo Kamatani and Masayuki Uchida;熊谷隆;熊谷隆;Hayato Kitagawa and Masayuki Uchida;石毛和弘
• 通讯作者: 石毛和弘

Blow-up set for a superlinear heat equation and pointedness of the initial data

超线性热方程的爆炸集和初始数据的指向性

• 发表时间: 2013
• 作者: Ichikawa H;K Kawai;S Yamamoto;and M Kameyama;Hidemitsu Wadade;藤嶋陽平
• 通讯作者: 藤嶋陽平