具加权非局部源反应扩散方程解的渐近行为

蒋良军

doi:10.13371/j.cnki.chin.q.j.m.2015.02.012

数学季刊 >

2015 , Vol. 30 >Issue 2: 244 - 252

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2015.02.012

具加权非局部源反应扩散方程解的渐近行为

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College of Mathematics and Information Technology, Nanjing Xiaozhuang University

JIANG Liang-jun(1961-), male, native of Guangan, Sichuan, a professor of Nanjing Xiaozhuang University, engages in partial differential equation.

收稿日期: 2013-07-09

网络出版日期: 2020-11-23

基金资助

Supported by the Natural Science Foundation of Jiangsu Province(BK2012072)；

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Asymptotic Analysis to a Diffusion Equation with a Weighted Nonlocal Source

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College of Mathematics and Information Technology, Nanjing Xiaozhuang University

JIANG Liang-jun(1961-), male, native of Guangan, Sichuan, a professor of Nanjing Xiaozhuang University, engages in partial differential equation.

Received date: 2013-07-09

Online published: 2020-11-23

Supported by

Supported by the Natural Science Foundation of Jiangsu Province(BK2012072)；

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摘要

In this paper,we deal with the blow-up property of the solution to the diffusion equation u_t= △u + a（x）f（u） ∫_Ωh（u）dx,x∈Ω,t>0 subject to the null Dirichlet boundary condition.We will show that under certain conditions,the solution blows up in finite time and prove that the set of all blow-up points is the whole region.Especially,in case of f（s） = s^p,h（s） = s^q,0 ≤ p≤1,p + q >1,we obtain the asymptotic behavior of the blow up solution.

关键词： asymptotic analysis; diffusion equation; global blow-up; nonlocal sources; weight function

本文引用格式

蒋良军 . 具加权非局部源反应扩散方程解的渐近行为[J]. 数学季刊, 2015 , 30(2) : 244 -252 . DOI: 10.13371/j.cnki.chin.q.j.m.2015.02.012

Abstract

Key words： asymptotic analysis; diffusion equation; global blow-up; nonlocal sources; weight function

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