Asymptotic behavior of zeros of solutions for parabolic equations

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 with a Caucy problem [GRAPHICS] 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 global solutions and prove that Z(t) subset of [-K, K] foe all t is an element of (0, T) with some K > 0 for each blowup solution, where T is the blowup time. (C) 2001 Academic Press.