一个带位势半线性方程爆破解的渐近行为

The characterization of the asymptotic behavior of the blow-up for a semilinear parabolic equation with a potential

主要研究半线性抛物方程ut=Δu+V(x)|u|p-1u爆破解的渐近行为.在本文中,假设N≥3并且1<p<N+2/N-2,初始值是有界的,V(x)∈C1(RN),且对任意x∈RN存在常数c和C使得c≤V(x)≤C成立.则当t→T时,对RN中的任意点a,(T-t)p1-1u(a+y(T-t)～(1/2),t)趋向于0或者±V(βa)β,(β=p-11).

This paper studies the asymptotic behavior of the solution near blow-up for the semilinear parabolic equation ut=△u＋V（x）｜u｜^p-1u in R^N × （0, T） with 0-Dirichlet condition. It assumes that,1〈p〈N＋2/N-2 or N≤2 and that the initial data is bounded,and v（x）∈ C^1（R^N） with c≤V（x）≤C for some positive constantc, Candall x∈R^N t→T for any point a in R^N.