Long-time dynamics of the Swift-Hohenberg equations


Khanmamedov A.

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, vol.483, no.2, 2020 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 483 Issue: 2
  • Publication Date: 2020
  • Doi Number: 10.1016/j.jmaa.2019.123626
  • Title of Journal : JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

Abstract

We consider the initial boundary value problems for the Swift-Hohenberg equation and its hyperbolic relaxation. Under the optimal conditions on the nonlinearity, we prove the well-posedness of the both problems and uniform (with respect to the initial data) global boundedness of the solutions. Then, we show that the both problems possess the global attractors of optimal regularity. (C) 2019 Elsevier Inc. All rights reserved.