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

2024/08/29 by Colli, Pierluigi, Sprekels, Jürgen · 1 citation
#35B40 #35M33 #35M87 #37D35 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2408.16332

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.

Cited by

• On the hyperbolic relaxation of the chemical potential in a phase field tumor growth model

Related

• On the optimal control of viscous Cahn-Hilliard systems with hyperbolic relaxation of the chemical potential
• On the longtime behavior of a viscous Cahn-Hilliard system with convection and dynamic boundary conditions
• On the viscous Cahn-Hilliard equation with singular potential and inertial term
• Solvability and sliding mode control for the viscous Cahn-Hilliard system with a possibly singular potential
• Asymptotic behavior of a nonisothermal viscous Cahn-Hilliard equation with inertial term