Convergence to equilibrium for time and space discretizations of the Cahn-Hilliard equation-Reference-Cited by-同舟云学术

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

Published:2022 Issue:8 Volume:15 Page:1987
ISSN:1937-1632
Container-title:Discrete and Continuous Dynamical Systems - S
language:
Short-container-title:DCDS-S

Author:

Brachet Matthieu¹,Parnaudeau Philippe²,Pierre Morgan¹

Affiliation:

1. Laboratoire de Mathématiques et Applications, Université de Poitiers, CNRS, F-86073 Poitiers, France

2. Institut Pprime, CNRS, UPR 3346, 11 Boulevard Marie et Pierre Curie, 86962 Futuroscope Chasseneuil Cedex, France

Abstract

<p style='text-indent:20px;'>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.</p>

Publisher

American Institute of Mathematical Sciences (AIMS)

Subject

Applied Mathematics,Discrete Mathematics and Combinatorics,Analysis

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