Upper semicontinuity of global attractors for the generalized Cahn-Hilliard equation with inertial term

Khanmamedov A., YAYLA S.

Journal of Mathematical Analysis and Applications, vol.560, no.2, 2026 (SCI-Expanded, Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 560 Issue: 2
  • Publication Date: 2026
  • Doi Number: 10.1016/j.jmaa.2026.130495
  • Journal Name: Journal of Mathematical Analysis and Applications
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH
  • Keywords: Cahn-Hilliard equation, Global attractor, Hyperbolic relaxation
  • Hacettepe University Affiliated: Yes

Abstract

In this paper, we consider the initial boundary value problem for the 2D Cahn-Hilliard equation involving inertial and zero-order source terms. In the case when the zero-order source term is a linear function on a large enough neighborhood of the origin, and the coefficient of the inertial term is sufficiently small, we prove that the global attractors for energy and weak solutions coincide. Then, we establish the upper semicontinuity of these global attractors.