Analysis on Singularities of Solutions to Nonlinear Partial Differential Equations

非线性偏微分方程解的奇异性分析

• 批准号: 11640173
• 负责人: NAGAI Toshitaka
• 金额: $ 2.24万
• 依托单位: Hiroshima University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 1999
• 资助国家: 日本
• 起止时间: 1999 至 2000
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-11640173/
• 关键词: Nonlinear partial differential equations; Advection-diffusion equations; Global solutions in time; Blowup solutions; Self-similar solutions; Stationary solutions; 放物型方程式系; 解の大域的存在; 解の特異性

The purpose of this research is to study the behavior of solutions to nonlinear partial differential equations by analyzing singularities of finite-time blowup solutions. Especially, we focus on two types of advection-diffusion equations (parabolic-elliptic system, parabolic system) and obtained the following results.1. The possibility of finite-time blowup of nonradial solutions to the parabolic-elliptic system.2. Finite-time blowup solutions to the parabolic system have δ-function singularities at isolated blow-up points in two-dimensional domains3. The structure of self-similar solutions to the parabolic system.4. The structure of steady states to the parabolic system.

本研究旨在通过分析有限时间爆破解的奇性来研究非线性偏微分方程解的性态。特别地，我们研究了两类对流扩散方程(抛物型椭圆型方程组和抛物型方程组)，得到了以下结果。抛物-椭圆型方程组非径向解的有限时间爆破的可能性。抛物型方程组的有限时间爆破解在二维域中孤立爆破点具有δ函数奇性。抛物型方程组自相似解的结构。抛物型系统的定态结构。

项目成果

N.Muramoto: "Existence of self-similar solutions to parabolic system modelling chemotaxis"J.J.Indust.Appl.Math.. 17. 427-451 (2000)

N.Muramoto：“抛物线系统建模趋化性的自相似解的存在”J.J.Indust.Appl.Math.. 17. 427-451 (2000)

T.Nagai: "Behavior of solutions to a parabolic-elliptic system modelling chemotaxis"J.Korean Math.Soc.. 37. 721-733 (2000)

T.Nagai：“模拟趋化性的抛物线-椭圆系统的解的行为”J.Korean Math.Soc.. 37. 721-733 (2000)

R.Ikehata: "The Palais-Smale condition for the energy of some semilinear parabolic equations"Hiroshima Math.J.. 30. 117-127 (2000)

R.Ikehata：“某些半线性抛物线方程能量的 Palais-Smale 条件”Hiroshima Math.J.. 30. 117-127 (2000)

T.Nagai: "Blowup of nonradial solutions to a parabolic-elliptic system modeling chemotaxis in two-dimensional domains"J.Inequal.Appl.. (to appear).

T.Nagai：“在二维域中模拟趋化性的抛物线椭圆系统的非径向解的放大”J.Inequal.Appl..（即将出现）。

T.Nagai: "Blowup of nonradial solutions to a parabolic-elliptic system modeling chemotaxis in two-dimensional domains"J.Inequal.Appl.. (発表予定).

T.Nagai：“在二维域中模拟趋化性的抛物线椭圆系统的非径向解的放大”J.Inequal.Appl..（待提交）。