2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/116668The large time behavior of non-negative solutions to the viscous Hamilton-Jacobi equation $u_t - Δu + |\nabla u|^q = 0$ in the whole space $R^N$ is investigated for the critical exponent $q = (N+2)/(N+1)$. Convergence towards a rescaled self-similar solution of the linear heat equation is shown, the rescaling factor being $(\log(t))^{-(N+1)}$. The proof relies on the construction of a one-dimensional invariant manifold for a suitable truncation of the equation written in self-similar variables.17 pages, no figureAnalysis of PDEs35B33; 35B40; 35K55; 37L25text