Stability for a class of nonlinear pseudo-differential equations

  title={Stability for a class of nonlinear pseudo-differential equations},
  author={Michael L. Frankel and Victor Roytburd},
  journal={Appl. Math. Lett.},
We study a class of nonlinear evolutionary equations generated by a pseudo-differential operator with the elliptic principal symbol and with nonlinearities of the form G(ux ) where cη2 ≤ G(η) ≤ Cη2 for large |η|. We demonstrate existence of a universal absorbing set, and a compact attractor, and show that the attractor is of a finite Hausdorff dimension. The stabilization mechanism is similar to the nonlinear saturation well known for the Kuramoto–Sivashinsky equation. c © 2007 Elsevier Ltd… CONTINUE READING

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