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

Abstract : 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 with the discretization is nonin-creasing 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 Lojasiewicz-Simon inequality.
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Paola F. Antonietti, Benoît Merlet, Morgan Pierre, Marco Verani. Convergence to equilibrium for a second-order time semi-discretization of the Cahn-Hilliard equation. AIMS Mathematics, AIMS Press, 2016, Nonlinear Evolution PDEs, Interfaces and Applications, 1 (3), pp.178-194. ⟨http://www.aimspress.com/journal/Math⟩. ⟨hal-01355956⟩

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