Abstract
In this paper, we investigate the large-times behavior of weak solutions to the fourth-order degenerate parabolic equation u t = −(| u| n u xxx ) x modeling the evolution of thin films. In particular, for all n > 0, we prove exponential decay of u( x, t) towards its mean value (1/|Ω|) ∫ Ω u dx in L 1-norm for long times and we give the explicit ( n-dependent) rate of decay. The result is based on classical entropy estimates, and on detailed lower bounds for the entropy production.
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