SHARP ANALYTIC–GEVREY REGULARITY ESTIMATESDOWN TO t = 0 FOR SOLUTIONS TO SEMILINEAR HEATEQUATIONS

摘要

We study the Gevrey regularity down to t = 0 of solutionsto the initial-value problem for the semilinear heat equation 6_tu — Δ_u+F[u] = 0 with polynomial non-linearities. The approach is based onsuitable iterative fixed point methods in L~p-based Banach spaces withanisotropic Gevrey norms with respect to the time and space variables.We also construct explicit solutions uniformly analytic in t > 0 andx E W for some conservative non-linear terms with symmetries.