Abstract :
This paper is concerned with solutions of ut − uxx = up, p > 1, defined in a cylinder QR = {(x, t): −R < x < R, 0 < t < 1} with R > 0, which blowup at t = 1. More precisely, we are interested in the asymptotic behaviour of such solutions near a blow-up point as t ↑ 1. We show that, whenever the blow-up set can be confined to the interior of the interval (−R, +R), asymptotics are the same as those corresponding to solutions defined in the whole line which assume bounded initial values. However, if the blow-up set reaches the boundary of the interval (−R, +R), a different behaviour may appear, as indicated by Theorem 2 in the Introduction.
