Long-time dynamics of the Cahn-Hilliard equation with kinetic rate dependent dynamic boundary conditions


Garcke H., Knopf P., YAYLA S.

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, vol.215, 2022 (Peer-Reviewed Journal) identifier identifier identifier

  • Publication Type: Article / Article
  • Volume: 215
  • Publication Date: 2022
  • Doi Number: 10.1016/j.na.2021.112619
  • Journal Name: NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
  • Journal Indexes: Science Citation Index Expanded, Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, Compendex, INSPEC, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
  • Keywords: Cahn-Hilliard equation, Dynamic boundary conditions, Long-time dynamics, Stability of global attractors, Robustness of exponential attractors, CONVERGENCE, BEHAVIOR, MODEL, EQUILIBRIUM, SYSTEM, ATTRACTORS, EVOLUTION, MEMORY

Abstract

We consider a Cahn-Hilliard model with kinetic rate dependent dynamic boundary conditions that was introduced by Knopf et al. (2021) and will thus be called the KLLM model. In the aforementioned paper, it was shown that solutions of the KLLM model converge to solutions of the GMS model proposed by Goldstein et al. (2011) as the kinetic rate tends to infinity. We first collect the weak well-posedness results for both models and we establish some further essential properties of the weak solutions. Afterwards, we investigate the long-time behavior of the KLLM model. We first prove the existence of a global attractor as well as convergence to a single stationary point. Then, we show that the global attractor of the GMS model is stable with respect to perturbations of the kinetic rate. Eventually, we construct exponential attractors for both models, and we show that the exponential attractor associated with the GMS model is robust against kinetic rate perturbations. (C) 2021 Elsevier Ltd. All rights reserved.