A note on a non-local Kuramoto-Sivashinsky equation

Jared C. Bronski, Razvan C. Fetecau, Thomas N. Gambill

Research output: Contribution to journalArticlepeer-review

Abstract

In this note we outline some improvements to a result of Hilhorst, Peletier, Rotariu and Sivashinsky [5] on the L2 boundedness of solutions to a non-local variant of the Kuramoto-Sivashinsky equation with additional stabilizing and destabilizing terms. We are able to make the following improvements: in the case of odd data we reduce the exponent in the estimate lim supt→∞ ||u|| < CLν from ν = 11/5 to ν = 3/2, and for the case of general initial data we establish an estimate of the above form with ν = 13/6. We also remove the restrictions on the magnitudes of the parameters in the model and track the dependence of our estimates on these parameters, assuming they are at least O(1).

Original languageEnglish (US)
Pages (from-to)701-707
Number of pages7
JournalDiscrete and Continuous Dynamical Systems
Volume18
Issue number4
StatePublished - Aug 1 2007

Keywords

  • Global attractors
  • Kuramoto-Sivashinsky equation

ASJC Scopus subject areas

  • Analysis
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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