On the dimension of the global attractor for a damped semilinear wave equation with critical exponent

We obtain in this paper a precise estimate of upper bound of the Hausdorff dimension of the global attractor for a damped semilinear wave equation wit h critical exponent. The obtained Hausdorff dimension decreases as the damp ing grows and is uniformly bounded for large damping, which conforms to phy sical intuition. The obtained results generalize and correct the correspond ing results obtained by Zhou recently. (C) 2000 American Institute of Physi cs. [S0022-2488(00)04705-8].