On Blow up at Space Infinity for Semilinear Heat Equations

A nonnegative blowing up solution of the semilinear heat equation ut = ¢u + up with p > 1 is considered when initial data u0 satisfies lim|x|→∞ 0 = M > 0, 0 ≤ 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 di®erential equation vt = vp with v(0) = M