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

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April 2005, 13(3): 553-560. doi: 10.3934/dcds.2005.13.553

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

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

Received July 2004 Revised November 2004 Published May 2005

Abstract
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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.

Keywords: Burgers equation., determining modes, global attractor, Inertial manifold.

Mathematics Subject Classification: 35B42, 35B41, 35K55, 35K15, 35G2.

Citation: Igor Kukavica. On Fourier parametrization of global attractors for equations in one space dimension. Discrete & Continuous Dynamical Systems - A, 2005, 13 (3) : 553-560. doi: 10.3934/dcds.2005.13.553

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