We study nonglobal positive solutions to the Dirichlet problem for u(t) = u(P) (Deltau + u) in bounded domains, where 0 < p < 2. It is proved that the set of points at which U blows up has positive measure and the blow-up rate is exactly (T - t)(-1/p). If either the space dimension is one or p < 1, the omega-limit set of (T - t)(1/p)u(t) consists of continuous functions solving Deltaw + w = 1/pw(1-p).. In one space dimension it is shown that actually (T - t)(1/p)u(t) --> w as t --> T, where w coincides with an element of a one-parameter family of functions inside each component of its positivity set; furthermore, we study the size of the components of {w > 0} with the result that this size is uniquely determined by Omega in the case p < 1, while for p > 1, the positivity set can have the maximum possible size 2pi/p for certain initial data, but it may also be arbitrarily close to the minimal length pi. (C) 2003 Elsevier Science (USA). All rights reserved. [References: 23]
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