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We are interested in nite-time blow-up phenomena for heat equations of the type: @u @t = u+ jujp 1u (1) where u : (x; t) 2 RN [0; T )! R, 1 < p, (N 2)p < N + 2. We rst construct for (1) a solution u which blows-up in nite time T at only one blow-up point x0 2 RN , and describe completely its blow-up pro le (or asymptotic behavior). This construction is based on a priori estimates' technique whi...
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ژورنال
عنوان ژورنال: Mathematische Annalen
سال: 1883
ISSN: 0025-5831,1432-1807
DOI: 10.1007/bf01443267