Optimal estimates for blowup rate and behavior for nonlinear heat equations

We first describe all positive bounded solutions of partial derivative w/partial derivative s = Delta w - 1/2y.del w - w/p - 1 + w(p) where (y, s) is an element of R-N x R, 1 < p, and (N - 2)p less than or equal to N + 2. We then obtain for blowup solutions u(t) of partial derivative u/partial derivative t = Delta u + u(p) uniform estimates at the blowup time and uniform space-time comparison with solutions of u' = u(p). (C) 1998 John Wiley & Sons, Inc.