Open AccessOn the dimension of global attractor for the Cahn-Hilliard-Brinkman system with dynamic boundary conditions
Author(s) -
Fang Li,
Bo You
Publication year - 2021
Publication title -
discrete and continuous dynamical systems. series b
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.864
H-Index - 53
eISSN - 1553-524X
pISSN - 1531-3492
DOI - 10.3934/dcdsb.2021024
Subject(s) - attractor , mathematics , dimension (graph theory) , lipschitz continuity , boundary (topology) , fractal dimension , phase space , space (punctuation) , mathematical analysis , hausdorff dimension , fractal , pure mathematics , physics , computer science , thermodynamics , operating system
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 \begin{document}$ \ell $\end{document} -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.