On blow-up at space infinity for semilinear heat equations

A nonnegative blowing up solution of the semilinear heat equation ut = Δu + up with p >1 is considered when initial data u0 satisfies lim |x|→∞ u0 =M >0, u0 M and u0 = M. It is shown that the solution blows up only at space infinity and that lim|x|→∞ u(x, t) is the solution of the ordinary differential equation vt = vp with v(0) =M.  2005 Elsevier Inc. All rights reserved