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

In w27x Fujita showed that for positive solutions, the initial value problem in RN . for utsDuqu p with p)1 exhibited the following behavior: If p-pcʹ 1q2rN, then the initial value problem does not have any nontrivial, non-negative solution existing on RN =w0, `. 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 w50x, 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.