Inserted: 20 dec 2012
Last Updated: 13 nov 2013
Journal: Ann. Inst. H. Poincaré Anal. Non Linéaire
We investigate large-time asymptotics for viscous Hamilton--Jacobi equations with possibly degenerate diffusion terms. We establish new results on the convergence, which are the first general ones concerning equations which are neither uniformly parabolic nor first order. Our method is based on the nonlinear adjoint method and the derivation of new estimates on long time averaging effects. It also extends to the case of weakly coupled systems.