数学季刊 ›› 2015, Vol. 30 ›› Issue (2): 244-252.doi: 10.13371/j.cnki.chin.q.j.m.2015.02.012
摘要: In this paper,we deal with the blow-up property of the solution to the diffusion equation ut = △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) = sp,h(s) = sq,0 ≤ p≤1,p + q >1,we obtain the asymptotic behavior of the blow up solution.
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