On Fourier parametrization of global attractors for equations in one space dimension

Igor Kukavica

doi:10.3934/dcds.2005.13.553

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2005, Volume 13, Issue 3: 553-560. Doi: 10.3934/dcds.2005.13.553

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On Fourier parametrization of global attractors for equations in one space dimension

Igor Kukavica^1,

1.
Department of Mathematics, University of Southern California, Los Angeles, CA 90089

Received: June 30, 2004

Revised: October 31, 2004

Published: March 2005

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Abstract

For the dissipative equations of the form

$ u_{t}-u_{x x}+f(x,u,u_x)=0$

we prove that the global attractor can be parametrized by a finite number of Fourier modes and that the number of modes is algebraic in parameters. This improves our earlier result [15], where the number of required modes is exponential. The method extends to equations of order higher than two.

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Mathematics Subject Classification: 35B42, 35B41, 35K55, 35K15, 35G20.

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