Let p > 1, alpha greater than or equal to 0, and p is an element of L' (R)
boolean AND L'(R) change its sign finite times. This paper is concerned wit
h a Caucy problem
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Define the set of zero a of a solution u by Z(t) = \x is an element of R ;
u(x, t) = 0\ for t > 0. In case of alpha = 0, we show that the set Z(t) is
contained in [-Ct, Ct] for large t > 0 with some C > 0 and that this order
of t is best possible. When alpha > 0, we also give estimates of Z(t) for g
lobal solutions and prove that Z(t) subset of [-K, K] foe all t is an eleme
nt of (0, T) with some K > 0 for each blowup solution, where T is the blowu
p time. (C) 2001 Academic Press.