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Convergence to equilibrium for a second-order time semi-discretization ofthe Cahn-Hilliard equation

Paola F. Antonietti Benoît Merlet Morgan Pierre Marco Verani

*Corresponding author: Morgan Pierre Morgan.Pierre@math.univ-poitiers.fr

Math2016,3,178doi:10.3934/Math.2016.3.178

We consider a second-order two-step time semi-discretization of the Cahn-Hilliard equation with an analytic nonlinearity. The time-step is chosen small enough so that the pseudo-energy associated withdiscretization is nonincreasing at every time iteration. We prove that the sequence generated by the scheme converges to a steady state as time tends to infinity. We also obtain convergence rates in the energy norm. The proof is based on the Łojasiewicz-Simon inequality.

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