On nonexistence of global solutions of some semilinear parabolic differential equations

The purpose of this paper is to show that the semilinear parabolic equation (a/3t)u--zlu+u 1/ has no global solutions for any nontrivial nonnegative initial data Uo(X) in case of N--2, a--1 or N=I, a--2, where N denotes the dimension of x-space.This problem was considered in Fujita H. [1] and in more general form [2]. The conclusions of [1] are as follows.In case of Na2 there does not exist a global solution for any nontrivial nonnegative initial data.On the other hand, in case of Na 2, there exists a global solution for sufficiently small initial data, and no global solutions for sufficiently large initial data.This paper will give a partial settlement for the case Na--2.We consider the next problem.-u(t,x)-zIu(t,x)+u(t,x) +"