Global attractor of the extended Fisher-Kolmogorov equation in Hk spaces

The long-time behavior of solution to extended Fisher-Kolmogorov equation is considered in this article. Using an iteration procedure, regularity estimates for the linear semigroups and a classical existence theorem of global attractor, we prove that the extended Fisher-Kolmogorov equation possesses a global attractor in Sobolev space Hk for all k > 0, which attracts any bounded subset of Hk (Ω) in the Hk -norm. 2000 Mathematics Subject Classification: 35B40; 35B41; 35K25; 35K30.