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

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March 2005, 4(1): 165-174. doi: 10.3934/cpaa.2005.4.165

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

1.	Department of Mathematical Analysis, Charles University, Prague, Sokolovská 83, 186 75 Prague 8, Czech Republic

Received January 2004 Revised October 2004 Published December 2004

Abstract
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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.

Keywords: nonlinear damping., global attractor, fractal dimension, wave equation, exponential attractor.

Mathematics Subject Classification: 37L25, 37L30, 35L7.

Citation: Dalibor Pražák. On the dimension of the attractor for the wave equation with nonlinear damping. Communications on Pure & Applied Analysis, 2005, 4 (1) : 165-174. doi: 10.3934/cpaa.2005.4.165

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