ON THE ASYMPTOTIC SHAPE OF BLOW-UP

For the semilinear parabolic equation u(t) = u(xx)+ e(u), we prove the existence of solutions which blow up in finite time and whose asymptotic shape near the blow up point approaches a nontrivial, nonsingular limit, in a suitable set of rescaled coordinates. Such asymptotic behavior is stable with respect to small perturbations of the initial conditions.