FINAL TIME BLOWUP PROFILES FOR SEMILINEAR PARABOLIC EQUATIONS VIA CENTER MANIFOLD THEORY

This paper considers the semilinear parabolic equation u(t) = DELTA-u + f(u) in R(n) x (0, infinity), where f(u) = e(u) or f(u) = u(p), p > 1. For any initial data that is a positive, radially decreasing lower solution, and that causes the corresponding solution u(x, t) to blow up at (0, T) is-an-element-of R(n) x (0, infinity), the authors prove by using techniques from center manifold theory that the final time blowup profiles satisfy u(x, T) = -2 ln Absolute value of x + ln Absolute value of ln x parallel-to + ln 8 + o(1) for f(u) = e(u), u(x, T) = (8-beta-2p Absolute value of ln x parallel-to/Absolute value of x 2)beta (1 + o(1)) for f(u) = u(p) as Absolute value of x --> 0.