Study on asymmetry and anisotropy in blow-up theory for nonlinear parabolic equations

非线性抛物方程爆炸理论中的不对称性和各向异性研究

• 批准号: 23654064
• 负责人: OZAWA Tohru
• 金额: $ 2.16万
• 依托单位: Waseda University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Challenging Exploratory Research
• 财政年份: 2011
• 资助国家: 日本
• 起止时间: 2011 至 2012
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-23654064/
• 关键词: 関数方程式の大域理論; 解の爆発; 非線型放物型方程式

Blow-up phenomenon of positive solutions to the Cauchy problem for nonlinear heat equation of Fujita type is studied. The blow-up phenomenon was first observed and proved by Hiroshi Fujita about half a century ago. There is a large literature on the subject, especially on the formation of blow-up solutions in configuration space up to the blow-up time. We have proved that the blow-up time is characterized by means of the spherical average of the Cauchy data. We removed the assumptions of uniformity and isotropy on the Cauchy data, which were necessary in the former works by Lee and Ni (Trans. Ams, 1992) and Gui and Wang (JDE 1995). We described how the ODE structure controls the blow-up phenomenon.

研究了非线性Fujita型热方程Cauchy问题正解的爆破现象。大约在半个世纪前，藤田浩首先观察到并证明了爆破现象。关于这个问题有大量的文献，特别是关于在位形空间中直到爆破时间的爆破解的形成。证明了爆破时间可用柯西数据的球平均来刻画。我们去掉了对柯西数据的均匀性和各向同性的假设，这些假设在Lee和Ni（Trans.Ams，1992）和Gui和Wang（JDE 1995）的以前的工作中是必要的。我们描述了ODE结构如何控制爆破现象。

项目成果

Scienceweb GCOE Sharp Morawetz estimates

Scienceweb GCOE Sharp Morawetz 估计

• 发表时间: 2013
• 作者: Kotani;M.;Imai;T.;Katayama;H.;Yui;Y.;Tange;Y.;Kaneda;H.;Nakagawa;T.;Enya;K.;Goo Ishikawa;Tohru Ozawa
• 通讯作者: Tohru Ozawa

Life span of positive solutions for a semilinear heat equation with general non-decaying initial data

具有一般非衰减初始数据的半线性热方程正解的寿命

• 发表时间: 2011
• 期刊: J. Math. Anal. Appl
• 作者: T. Ozawa;Y. Yamauchi
• 通讯作者: Y. Yamauchi

Life span of positive solutions for a semilinear heat equation with nondecaying initial data

具有非衰减初始数据的半线性热方程正解的寿命

• 发表时间: 2012
• 作者: Tanaka;K.E.I.;Nakamoto;T.;Shinya Nishibata;Yusuke Yamauchi
• 通讯作者: Yusuke Yamauchi

Finite charge solutions to cubic Schrodinger equations with a nonlocal nonlinearity in one space dimension

一维非局部非线性三次薛定谔方程的有限电荷解

• 发表时间: 2013
• 期刊: Discrete and Continuous Dynamical Systems A
• 作者: K. Nakamura;T. Ozawa
• 通讯作者: T. Ozawa

無限遠方にて減衰しない初期値に対する熱方程式の解の爆発時刻に関する指向性を持つ評価

无限距离不衰减初始值的热方程解的爆炸时间的定向评估

• 发表时间: 2011
• 作者: Wada;K.;Tanaka;H.;Suyama;T.;Kimura;H.;and Yamamoto;T.;Sumio Yamada;山内雄介
• 通讯作者: 山内雄介