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Quasi-periodic solutions for completely resonant non-linear wave equations in 1D and 2D
On Fourier parametrization of global attractors for equations in one space dimension
| 1. | Department of Mathematics, University of Southern California, Los Angeles, CA 90089 |
$ 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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