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

In [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 ppc, 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...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications 2000-03, Vol.243 (1), p.85-126
Main Authors: Deng, Keng, Levine, Howard A.
Format: Article
Language:English
Subjects:
Exact sciences and technology
Mathematical analysis
Mathematics
Ordinary differential equations
Partial differential equations
Sciences and techniques of general use
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Summary:In [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 ppc, 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.
ISSN:0022-247X
1096-0813
DOI:10.1006/jmaa.1999.6663