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We prove a lower bound on the rate of relaxation to equilibrium in the H 1 norm for a thin fllm equation. We flnd a two stage relaxation, with power law decay in an initial interval, followed by exponential decay, at an essentially optimal rate, for large times. The waiting time until the exponential decay sets in is explicitly estimated.

An Entropy Dissipation-Entropy Estimate for a Thin Film Type Equation