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Open Access Research

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

Hong Luo

Author Affiliations

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:10.1186/1687-2770-2011-39

Published: 25 October 2011

Abstract

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.

Keywords:
semigroup of operator; global attractor; extended Fisher-Kolmogorov equation; regularity