Abstract: The initial value problem in Rⁿ is discussed,
u_t(x,t)-△u(x,t)=u^p(x,t)-u(x,t), u(x,0)=φ(x) ≥ 0.
where p>1. It is well known that the solution u(x, t) blows up in finite time for some initial values φ. In this paper, it is proved that the blow-up occurs only at point x=0 for some special initial values φ(x).