Exponential decay of solutions for the convective Cahn-Hilliard equation with the inertial term

Khanmamedov A.

Journal of Mathematical Analysis and Applications, vol.561, no.2, 2026 (SCI-Expanded, Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 561 Issue: 2
  • Publication Date: 2026
  • Doi Number: 10.1016/j.jmaa.2026.130578
  • Journal Name: Journal of Mathematical Analysis and Applications
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH
  • Keywords: Convective Cahn-Hilliard equation, Exponential decay, Hyperbolic relaxation
  • Hacettepe University Affiliated: Yes

Abstract

In this paper, we consider the initial boundary value problem for the two-dimensional convective Cahn-Hilliard equation involving the inertial term. Using the semigroup theory and Brezis-Gallouet inequality, we first establish the existence of a unique weak solution. Then, using the splitting method, we prove that if the coefficient of the inertial term is sufficiently small, the weak solution exhibits exponential decay, and the decay rate is independent of the inertial term's coefficient.