Dynamics of Partial Differential Equations

Volume 13 (2016)

Number 1

Dedicated to emeritus associate editor Shiyi Chen

Well-posedness and global attractor of the Cahn–Hilliard–Brinkman system with dynamic boundary conditions

Pages: 75 – 90

DOI: http://dx.doi.org/10.4310/DPDE.2016.v13.n1.a4

Authors

Bo You (School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, China)

Fang Li (Department of Mathematics, Nanjing University, Nanjing, China)

Abstract

Our aim in this paper is to study the well-posedness and the longtime behavior of solutions for the Cahn–Hilliard–Brinkman system with dynamic boundary conditions. We prove the well-posedness of solutions and the existence of a global attractor in $H^1(\bar{\Omega}, d \nu)$ for the Cahn–Hilliard–Brinkman system with dynamic boundary conditions by using Aubin–Lions compactness Theorem.

Keywords

global attractor, Cahn–Hilliard–Brinkman system, dynamic boundary conditions, dissipativity, Aubin–Lions compactness theorem

2010 Mathematics Subject Classification

35-xx, 37-xx

Full Text (PDF format)

Published 29 March 2016