## Abstract

In this note we outline some improvements to a result of Hilhorst, Peletier, Rotariu and Sivashinsky [5] on the L_{2} 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 sup_{t→∞} ||u|| < CL^{ν} 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 language | English (US) |
---|---|

Pages (from-to) | 701-707 |

Number of pages | 7 |

Journal | Discrete and Continuous Dynamical Systems |

Volume | 18 |

Issue number | 4 |

State | Published - Aug 1 2007 |

## Keywords

- Global attractors
- Kuramoto-Sivashinsky equation

## ASJC Scopus subject areas

- Analysis
- Discrete Mathematics and Combinatorics
- Applied Mathematics