# American Institute of Mathematical Sciences

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

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.

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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