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

Fang Li; Bo You

doi:10.3934/dcdsb.2021024

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2021, Volume 26, Issue 12: 6387-6403. Doi: 10.3934/dcdsb.2021024 open access

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

Fang Li^1, and
Bo You^2, ,

1.
School of Mathematics and Statistics, Xidian University, Xi'an, 710126, China
2.
School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an, 710049, China

^* Corresponding author: youb2013@xjtu.edu.cn(B. You)
^* Corresponding author: youb2013@xjtu.edu.cn(B. You)

Received: July 2020

Revised: December 2020

Early access: January 2021

Published: December 2021

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Abstract

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 $ \ell $-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 mapping from the auxiliary normed space into the original phase space.

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Mathematics Subject Classification: 35B41, 35Q35, 37L30.

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