Global attractor of the extended Fisher-Kolmogorov equation in Hk spaces
College of Mathematics, Sichuan University, Chengdu, Sichuan 610041, PR China
College of Mathematics and Software Science, Sichuan Normal University, Chengdu, Sichuan 610066, PR China
Boundary Value Problems 2011, 2011:39 doi:10.1186/1687-2770-2011-39Published: 25 October 2011
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.