COMPLETE BLOW-UP AND ESTIMATE ON THE LOCALIZATION FOR A QUASILINEAR PARABOLIC EQUATION WITH NONLINEAR SOURCE

Abstract

This paper deals with the Cauchy problem for a quasilinear parabolic equation with nonlinear source [Formula: see text] where N ≥ 1, p > 2, m, l, q > 1 and T < ∞ is blow-up time. When q > l + m(p - 2) + p, we first give an upper bound estimate on the localization in terms of the initial support supp u0(x) and the blow-up time T < ∞ provided that the initial function u0(x) is compactly supported. Moreover, for the special case m = l, when [Formula: see text], we obtain the result of complete blow-up and the stability of complete blow-up time provided that the solution u(x, t) blows up in finite time.