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

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