一个带加权使局部源抛物型方程解的整体爆破

摘要

The paper deals with the blow-up property of the solution to the parabolic equation ut=Δu＋a（x）epu＋qu（x0,t）,x∈Ω,t〉0 subject to the null Dirichlet boundary condition.It has been proved that when p〈0 with p＋q〉0,the solution blows up everywhere in Ω.%考虑带齐次Dirichlet边界条件,具使局部源项的抛物型方程ut=Δu＋a（x）epu＋qu（x0,t）,x∈Ω,t〉0的解的爆破性质,我们证明了当p〈0且p＋q〉0时,解在Ω内处处爆破.