Structure of nonnegative sloutions of diffusive equetious and its applications

扩散方程的非负表述结构及其应用

• 批准号: 12640206
• 负责人: ISHIGE Kazuhiro
• 金额: $ 1.86万
• 依托单位: Nagoya University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2000
• 资助国家: 日本
• 起止时间: 2000 至 2001
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-12640206/
• 关键词: heat ezuation.; blow-up prololem; neumann condition; nonneqstibe solution; コーシー問題

We study the uniqueness of nonnegative solutions of the diffusive equations in unbounded domains. We first study the problem with Minoru Murata, and obtain an optimal sufficient condition for the uniqueness of the nonnegative solutions of the whole Euclidean space to hold. Furthermore Ishige study the uniqueness of nonnegative solutions of the Cauchy-Dirichlet problem to the diffusive equations in unbounded domains, and obtain an optimal sufficient condition for the uniiqueness tohold.Next we study the blow-up problem for a semilinear parabolic equation with larqe diffusion. We prove that the solution blows up only near some points determined by the projection of the initial data to the second Neumann eigenspace. In order to study this problem, we need to study the long-time behavior of the nonnegative solution of the heat equation, that is, the Neumann eigenfunctions.

我们研究无界域中扩散方程非负解的唯一性。我们首先研究了村田稔问题，得到了整个欧氏空间非负解唯一性成立的最优充分条件。此外，Ishige还研究了无界域中扩散方程的Cauchy-Dirichlet问题非负解的唯一性，并得到了保持唯一性的最优充分条件。接下来我们研究具有大扩散的半线性抛物型方程的爆炸问题。我们证明，解仅在由初始数据到第二诺依曼本征空间的投影确定的某些点附近爆炸。为了研究这个问题，我们需要研究热方程非负解的长期行为，即诺依曼本征函数。

项目成果

Kazuhiro Ishige: "Blow-up time and blow-up set of the solutions for semilinear cheat equations with large diffucion"Suni-Kaiseki-Ken Kokyuvoku. 1237. 120-135 (2001)

Kazuhiro Ishige：“具有大扩散的半线性作弊方程解的爆炸时间和爆炸集”Suni-Kaiseki-Ken Kokyuvoku。

Kazuhiro Ishige: "Blow-up Time and blow-up set of the solutions for semilinear heat equations with large diffusion"数理解析研講究録. 1237. 120-135 (2001)

Kazuhiro Ishige：“大扩散半线性热方程解的爆炸时间和爆炸集”数学分析研究报告。1237。120-135（2001）。

Kazuhiro Ishige: "Blow-up time and blow-up set of the solutions for semilinear heat equations with large diffusion"Advances in Differential Equations. 7. 1003-1024 (2002)

Kazuhiro Ishige：“具有大扩散的半线性热方程解的爆炸时间和爆炸集”微分方程的进展。

Kazuhiro Ishige, Minoru Murata: "Uniqueness of nonnegative solution of the Coucling problem for parabolic equation on manifolds and domains"Anrali della Scuola Normale Superiore, Classed : Sciense. 30. 171-223 (2001)

Kazuhiro Ishige、Minoru Murata：“流形和域上抛物线方程的 Coucling 问题非负解的唯一性”Anrali della Scuola Superiore，分类：科学。

Kazuhiro Ishige and Minoru Murata: "Uniqueness of nonvaqative salutions of the Canchy problem for parabolic equationg on manifolds and domains."Anirali della Scuola Normale Superiorc Classe d : Sciense. 30. 171-223 (2001)

Kazuhiro Ishige 和 Minoru Murata：“流形和域上抛物线方程 Canchy 问题的非真空解的独特性。”Anirali della Scuola Normale Superiorc Classe d：科学。