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- W2079786066 abstract "In [ 27 ] Fujita showed that for positive solutions, the initial value problem (in R N ) for u t = Δ 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 × [0, ∞) (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." @default.
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- W2079786066 date "2000-03-01" @default.
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- W2079786066 title "The Role of Critical Exponents in Blow-Up Theorems: The Sequel" @default.
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- W2079786066 doi "https://doi.org/10.1006/jmaa.1999.6663" @default.
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