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

Dalibor Pražák

doi:10.3934/cpaa.2005.4.165

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2005, Volume 4, Issue 1: 165-174. Doi: 10.3934/cpaa.2005.4.165

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

Dalibor Pražák^1,

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

Received: January 2004

Revised: October 2004

Published: March 2005

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Abstract

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.

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Mathematics Subject Classification: 37L25, 37L30, 35L70.

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