Shape of the solutions and asymptotic analysis for the diffusive equations

扩散方程解的形状和渐近分析

• 批准号: 19340036
• 负责人: ISHIGE Kazuhiro
• 金额: $ 11.48万
• 依托单位: Tohoku University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (B)
• 财政年份: 2007
• 资助国家: 日本
• 起止时间: 2007 至 2010
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-19340036/
• 关键词: 熱方程式; 最大点挙動; 等高面; 大域的挙動; 爆発問題; 解の形; 漸近展開; 解の凸性; 解の形状; 漸近挙動; 符号変化する解; 解の最大点挙動; 解の微分係数の減衰

We study the shapes of the solutions of diffusive equations, and reveal the relationship between the movement of hot spots and the harmonic functions. Furthermore we studied the asymptotics of the solutions for the semilinear heat equations. In particular, we characterized the location of blow-up set for blow-up solutions, and also gave the decay estimates of the deference between global in time solutions and their asymptotics.

我们研究扩散方程解的形状，并揭示热点运动与调和函数之间的关系。此外，我们研究了半线性热方程解的渐近性。特别是，我们描述了爆炸解的爆炸集的位置，并给出了全局时间解与其渐进性之间差异的衰减估计。

项目成果

Parabolic quasi-concavity for solutions to parabolic problems in convex rings

用于解决凸环抛物线问题的抛物线拟凹性

• 发表时间: 2010
• 作者: Kazuhiro Ishige;Paolo Salani
• 通讯作者: Paolo Salani

Hot spots for the heat equation with a rapidly decaying negative potential

具有快速衰减负势的热方程的热点

• 发表时间: 2009
• 作者: Kazuhiro Ishige;Yoshitsugu Kabeya
• 通讯作者: Yoshitsugu Kabeya

Global solutions of the heat equation with a nonlinear boundary condition

具有非线性边界条件的热方程的全局解

• 发表时间: 2010
• 影响因子: 2.1
• 作者: Kazuhiro Ishige; Tatsuki Kawakami
• 通讯作者: Tatsuki Kawakami

Convexity breaking of the free boundary for porous medium equations

多孔介质方程自由边界的凸破断

• 发表时间: 2011
• 作者: 石毛和弘

Large time behaviors of hot spots for the heat equation with a potential

具有势能的热方程热点的大时间行为

• 发表时间: 2007
• 作者: Kazuhiro Ishige; Yoshitsugu Kabeya
• 通讯作者: Yoshitsugu Kabeya