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On the dimension of the attractor for the wave equation with nonlinear damping
We give an explicit estimate of the fractal dimension
of the global attractor to the wave
equation with nolinear damping.
The nonlinearities are smooth functions
of certain polynomial growth.
As a by-product we estimate the dimension of
the exponential attractor for the time $\tau$
solution operator provided that $\tau$ is
The main tool used in the proof
is the so-called method of the trajectories.