Asymptotic behavior for a viscous Hamilton-Jacobi equation with critical exponent Thierry GallayPhilippe Laurencot 35B3335B4035K5537L25diffusive Hamilton-Jacobi equationlarge time behaviorcritical exponentabsorptioninvariant manifoldself-similarity The large time behavior of non-negative solutions to the viscous Hamilton-Jacobi equation $\partial_t u - \Delta u + |\nabla u|^q = 0$ in $(0,\infty) \times \mathbb{R}^N$ is investigated for the critical exponent $q = (N+2)/(N+1)$. Convergence towards a rescaled self-similar solution to the linear heat equation is shown, the rescaling factor being $(\ln{t})^{-(N+1)}$. The proof relies on the construction of a one-dimensional invariant manifold for a suitable truncation of the equation written in self-similar variables. Indiana University Mathematics Journal 2007 text pdf 10.1512/iumj.2007.56.3107 10.1512/iumj.2007.56.3107 en Indiana Univ. Math. J. 56 (2007) 459 - 480 state-of-the-art mathematics http://iumj.org/access/