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