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

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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.

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


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