“…Motivated by the behavior of the solutions to the viscous Burgers equation with linear diffusion (1.7) (see, for instance, [14,20,21,23,27,29]), in Section 4 we investigate the phenomenon of metastability (whereby the time dependent solution reaches its asymptotic configuration in an exponentially, with respect to ε 1, long time interval) in the case of a nonlinear diffusion. In particular, we show that a metastable behavior also appears for the solutions to (1.1) with dissipation fluxes (1.4), (1.5) (the case of the mean curvature operator in the Euclidean space (1.3) has been recently studied in [11]); in these cases condition (1.10) becomes…”