Blow-up of solutions of supercritical semilinear parabolic equations

Abstract

We consider the equation (E) u(t) = Δu + u(p) where x Є R(N) (N ≥ 1), t > 0, p > 1. We show that if N ≥ 11 and p > N - 2 (N - 1)1/2/(N - 4) - 2(N - 1)1/2 then there exist radial and positive solutions of (E) which blow up at x = 0, t = T < ∞ and such that GRAPHICS Precise asymptotics for these solutions near t = T are also obtained