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On the dimension of the attractor for the wave equation with nonlinear damping

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  • 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 sufficiently large. The main tool used in the proof is the so-called method of the trajectories.
    Mathematics Subject Classification: 37L25, 37L30, 35L70.

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