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Article Dans Une Revue Discrete and Continuous Dynamical Systems - Series S Année : 2022

Convergence to equilibrium for time and space discretizations of the Cahn-Hilliard equation

Résumé

We review space and time discretizations of the Cahn-Hilliard equation which are energy stable. In many cases, we prove that a solution converges to a steady state as time goes to infinity. The proof is based on Lyapunov theory and on a Lojasiewicz type inequality. In a few cases, the convergence result is only partial and this raises some interesting questions. Numerical simulations in two and three space dimensions illustrate the theoretical results. Several perspectives are discussed.

Dates et versions

hal-03828872 , version 1 (25-10-2022)

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Matthieu Brachet, Philippe Parnaudeau, Morgan Pierre. Convergence to equilibrium for time and space discretizations of the Cahn-Hilliard equation. Discrete and Continuous Dynamical Systems - Series S, 2022, 15 (8), pp.1987. ⟨10.3934/dcdss.2022110⟩. ⟨hal-03828872⟩
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