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

Abstract

<p style='text-indent:20px;'>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 <inline-formula><tex-math id="M1">\begin{document}$ \ell $\end{document}</tex-math></inline-formula>-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.</p>