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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

Igor Kukavica 1,

1. 

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

Received  July 2004 Revised  November 2004 Published  May 2005

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