We prove a lower bound on the rate of realaxation to equililbrium in the H1 norm for a thin film equation. We find a two stagerelaxation, with power law decay in an initial interval followed byexponential decay, at an essentially optimal rate, for large times. The waiting time until the expoential decay sets in is explicitly estimated.
"An Entropy Dissipation-Entropy Estimate for a Thin Film Type Equation." Commun. Math. Sci. 3 (2) 171 - 178, June 2005.