Abstract
Abstract In this paper, we study the ivp(initial value problem) for a nonnegative function u(t,x)≥0 : ( u_t=∆u+u^(1+α),x∈R^m,t>0 and u(x,0)=a(x),x∈R^m ) where α> 0 is a constant and the initial date a(x)>0 is given(a(x) is not identically zero ). We prove the following two results : if 0 <m α< 2, there is no global solution of the ivp defined for all time t∈[0;∞) ; on the other hand, if m α>2, there exists initial data a(x) so that the ivp has a global solution defined for all time t∈[0;∞)