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