WIAS Preprint No. 3128, (2024)

Hyperbolic relaxation of the chemical potential in the viscous Cahn--Hilliard equation


Authors

  • Colli, Pierluigi
    ORCID: 0000-0002-7921-5041
  • Sprekels, Jürgen
    ORCID: 0009-0000-0618-8604

2020 Mathematics Subject Classification

  • 35M33 35M87 35B40 37D35

Keywords

  • Cahn--Hilliard system, hyperbolic relaxation, partial differential equations, initial-boundary value problem, well-posedness, continuous dependence, regularity, asymptotic convergence

DOI

10.20347/WIAS.PREPRINT.3128

Abstract

In this paper, we study a hyperbolic relaxation of the viscous Cahn--Hilliard system with zero Neumann boundary conditions. In fact, we consider a relaxation term involving the second time derivative of the chemical potential in the first equation of the system. We develop a well-posedness, continuous dependence and regularity theory for the initial-boundary value problem. Moreover, we investigate the asymptotic behavior of the system as the relaxation parameter tends to 0 and prove the convergence to the viscous Cahn--Hilliard system.

Download Documents