The existence of global attractor for a fourth-order parabolic equation

Abstract

This article is concerned with a fourth-order parabolic equation. Based on the regularity estimates for the semigroups and the classical existence theorem of global attractors, we prove that the fourth-order parabolic equation possesses a global attractor in H ^k (0 ≤ k < 5) space, which attracts any bounded subset of H ^k (Ω) in the H ^k -norm.

Keywords:

• global attractor
• fourth-order parabolic equation
• absorbing set
• ω-limit set

AMS Subject Classifications:

• 35B41
• 35K35
• 76A20

Acknowledgements

The authors would like to thank the referees for the valuable comments and suggestions about this article.