The role of critical exponents in blow-up theorems: The sequel

In [27] Fujita showed that for positive solutions, the initial value problem (in R-N) for u(t) = Delta u + u(p) with p > 1 exhibited the following behavior: If p < p(c) = 1 + 2/N, then the initial value problem does not have any nontrivial, non-negative solution existing on R-N X [0, infinity) (a global solution), whereas if p > p(c), there exist global, small data, positive solutions as well as solutions which are non-global, We call such a result a blow-up theorem of Fujita type. In [50], Levine discussed the various theorems of this type that had appeared in the literature prior to 1990. In this paper we revisit the literature since 1990. (C) 2000 Academic Press.