On the dimension of global attractor for the Cahn-Hilliard-Brinkman system with dynamic boundary conditions

Fang Li, ,School of Mathematics and Statistics, Xidian University, Xi'an, 710126, China, Bo You, ,School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an, 710049, China
2017 Discrete and continuous dynamical systems. Series B  
The objective of this paper is to study the fractal dimension of global attractor for the Cahn-Hilliard-Brinkman system with dynamic boundary conditions. Inspired by the idea of the -trajectory method, we prove the existence of a finite dimensional global attractor in an auxiliary normed space for the Cahn-Hilliard-Brinkman system with dynamic boundary conditions and estimate the fractal dimension of the global attractor in the original phase space for this system by defining a Lipschitz
more » ... a Lipschitz mapping from the auxiliary normed space into the original phase space. 2020 Mathematics Subject Classification. 35B41, 35Q35, 37L30.
doi:10.3934/dcdsb.2021024 fatcat:u5ssj7osmzc6fjsrhszcn56b6u