On a Cahn–Hilliard/Allen–Cahn system coupled with a type III heat equation and singular potentials. (July 2020)

• Record Type: Journal Article
• Authors: Makki, Ahmad; Miranville, Alain; Saoud, Wafa
• Is Part Of: Nonlinear analysis. Volume 196(2020)
• Publication Date: 2020-07
• Subjects: 35B45, 35K55, 35L15; Cahn–Hilliard/Allen–Cahn equations -- Type III heat conduction -- Logarithmic nonlinear terms -- Well-posedness -- Dissipativity; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2020.111804
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: Our aim in this article is to study the asymptotic behavior of a Cahn–Hilliard/Allen–Cahn system coupled with a heat equation based on the type III heat conduction law with singular potentials. We also show further regularity results and we prove a strict separation property (from the pure states) in one space dimension.