On the degenerate Cahn–Hilliard equation: Global existence and entropy estimates of weak solutions

Article type: Research Article

Authors: Jihui, Wu^{a; *} | Shu, Wang^b

Affiliations: [a] Center of Intelligent Computing and Applied Statistics, College of Mathematics, Physics and Statistics, Shanghai University of Engineering Science, Shanghai 201620, P. R. China | [b] School of Mathematics and Information Sciences, Guangzhou University, Guangzhou, 510006, China

Correspondence: [*] Corresponding author. E-mail: wujh225@163.com.

Abstract: In this paper, we consider a class of the degenerate Cahn–Hilliard equation with a smooth double-well potential. By applying a semi-discretization technique and asymptotic analysis method on non-degenerate Cahn–Hilliard equation, we obtain the existence and regularity of weak solutions to the Cahn–Hilliard equation with degenerate mobility. Moreover, we define a new entropy and obtain the global entropy estimates.

Keywords: Degenerate, non-degenerate, semi-discretization, entropy

DOI: 10.3233/ASY-191563

Journal: Asymptotic Analysis, vol. 119, no. 1-2, pp. 1-38, 2020