Stability for a class of nonlinear pseudo-differential equations

@article{Frankel2008StabilityFA,
  title={Stability for a class of nonlinear pseudo-differential equations},
  author={Michael L. Frankel and Victor Roytburd},
  journal={Appl. Math. Lett.},
  year={2008},
  volume={21},
  pages={425-430}
}
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

From This Paper

Topics from this paper.

Citations

Publications citing this paper.

References

Publications referenced by this paper.
Showing 1-10 of 14 references

Some global dynamical properties of the Kuramoto–Sivashinsky equations: Nonlinear stability and attractors

  • B. Nicolaenko, B. Scheurer, R. Temam
  • Physica D 16
  • 1985
Highly Influential
4 Excerpts

Weakly nonlinear asymptotics of the κ–θ model of cellular flames: The QS equation

  • C.-M. Brauner, M. Frankel, J. Hulshof, G. I. Sivashinsky
  • Interfaces Free Bound 7
  • 2005
1 Excerpt

Stability of the Kuramoto–Sivashinsky and related systems

  • J. Goodman
  • Comm. Pure Appl. Math. 47
  • 1994
1 Excerpt

A global attracting set for the Kuramoto–Sivashinsky equation

  • P. Collet, J.-P. Eckmann, H. Epstein, J. Stubbe
  • Comm. Math. Phys. 152
  • 1993
1 Excerpt

Approximate equations for long nonlinear waves on a viscous film

  • J. Topper, T. Kawahara
  • J. Phys. Soc. Japan 44
  • 1978
1 Excerpt

Diffusion induced chaos in reactions systems

  • Y. Kuramoto
  • Progr. Theoret. Phys. Suppl. 64
  • 1978
1 Excerpt

Similar Papers

Loading similar papers…