CLASSIFICATION OF SINGULARITIES FOR BLOWING-UP SOLUTIONS IN HIGHER DIMENSIONS

Consider the Cauchy problem [GRAPHICS] where p > 1, and u0(x) is a continuous, nonnegative and bounded function. It is known that, under fairly general assumptions on u0(x) , the unique solution of (P), u(x, t), blows up in a finite time, by which we mean that [GRAPHICS] In this paper we shall assume that u(x, t) blows up at x = 0, t = T < +infinity, and derive the possible asymptotic behaviours of u(x, 1) as (x, t) --> (0, T), under general assumptions on the blow-up rate.