Exponential Attractors for the Viscous Cahn-Hilliard System

Abstract

In this article, we explore a viscous Cahn-Hilliard system, which has applications in biology. By imposing appropriate boundary and initial conditions, we examine the asymptotic behavior of its solutions. First, we show that the problem of initial and limit values generates by a continuous semigroup on an appropriate phase space, which has a global attractor denoted $\mathcal{A}$. Subsequently, we establish the existence of an exponential attractor $\mathcal{M}$. Therefore, the global attractor $\mathcal{A}$ has a finite fractal dimension.