The Role of Critical Exponents in Blow-Up Theorems: The Sequel

AbstractIn [27] Fujita showed that for positive solutions, the initial value problem (in RN) for ut=Δu+up with p>1 exhibited the following behavior: If p<pc≡1+2/N, then the initial value problem does not have any nontrivial, non-negative solution existing on RN×[0,∞) (a global solution), whereas if p>pc, 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