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Preprints, Working Papers, ... Year : 2021

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

Abstract

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.
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Dates and versions

hal-03466113 , version 1 (04-12-2021)

Identifiers

  • HAL Id : hal-03466113 , version 1

Cite

Matthieu Brachet, Philippe Parnaudeau, Morgan Pierre. Convergence to equilibrium for time and space discretizations of the Cahn-Hilliard equation. 2021. ⟨hal-03466113⟩
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