Estimates on the dimension of an attractor for a nonclassical hyperbolic equation

In this paper, we estimate the dimension of a global attractor for a nonclassical hyperbolic equation with a viscoelastic damping term in Hilbert spaces $H_{0}^{2}\times L^{2}$ and $D(A)\times H_{0}^{2}$, where $D(A)=\{v\in H_{0}^{2}\mid Av\in L^{2}\}$ and $A=\Delta^{2}$. We obtain an explicit formula of the upper bound of the dimension of the attractor. The obtained dimension decreases as damping grows and is uniformly bounded for large damping, which conforms to physical intuition.