Rigorous Numerics for Partial Differential Equations: The Kuramoto-Sivashinsky Equation

@article{Zgliczynski2001RigorousNF,
  title={Rigorous Numerics for Partial Differential Equations: The Kuramoto-Sivashinsky Equation},
  author={Piotr Zgliczynski and Konstantin Mischaikow},
  journal={Foundations of Computational Mathematics},
  year={2001},
  volume={1},
  pages={255-288}
}
We present a new topological method for the study of the dynamics of dissipative PDE’s. The method is based on the concept of the selfconsistent apriori bounds, which allows to justify rigorously the Galerkin projection. As a result we obtain a low-dimensional system of ODE’s subject to rigorously controlled small perturbation from the neglected modes. To this ODE’s we apply the Conley index to obtain information about the dynamics of the PDE under consideration. We applied the method to the… CONTINUE READING
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