Geodesic
Estimates on the dimension of an attractor for a nonclassical hyperbolic equation
Wu, Delin1 ; Zhong, Chengkui1
1 School of Mathematics and Statistics, Lanzhou University, Lanzhou, 730000, P. R. China
Electronic research announcements of the American Mathematical Society, Tome 12 (2006), pp. 63-70 Cet article a éte moissonné depuis la source American Mathematical Society

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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.
DOI : 10.1090/S1079-6762-06-00162-4

Wu, Delin 1 ; Zhong, Chengkui 1

1 School of Mathematics and Statistics, Lanzhou University, Lanzhou, 730000, P. R. China 
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Wu, Delin; Zhong, Chengkui. Estimates on the dimension of an attractor for a nonclassical hyperbolic equation. Electronic research announcements of the American Mathematical Society, Tome 12 (2006), pp. 63-70. doi: 10.1090/S1079-6762-06-00162-4

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