Asymptotic Analysis to a Diffusion Equation with a Weighted Nonlocal Source

JIANG Liang-jun

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

Chinese Quarterly Journal of Mathematics >

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

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

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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Abstract

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.

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

Cite this article

JIANG Liang-jun . Asymptotic Analysis to a Diffusion Equation with a Weighted Nonlocal Source[J]. Chinese Quarterly Journal of Mathematics, 2015 , 30(2) : 244 -252 . DOI: 10.13371/j.cnki.chin.q.j.m.2015.02.012

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