Abstract

We describe the asymptotic behavior as t ? ? of the solution of ut = ?pu in IRN, for (2N + 1)/(N + 1) ? p < N and non-negative, integrable initial data. Optimal rates in L q, q = 2 - 1/(p - 1) for the convergence towards a self-similar profile corresponding to a solution with Dirac distribution initial data are found. They are connected with optimal constants for a Gagliardo-Nirenberg inequality.