Formal solutions of semilinear heat equations

We study formal power series solutions to the initial value problem for semilinear heat equation ∂tu − u = f (u) with polynomial nonlinearity f and prove that they belong to the formal Gevrey class G2. Next we give counterexamples showing that the solution, in general, is not analytic in time at t = 0. © 2007 Elsevier Inc. All rights reserved.