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Attractor bifurcation for extended Fisher-Kolmogorov equation. (English) Zbl 1293.35050

Summary: We consider the asymptotic stability and attractor bifurcation of the extended Fisher-Kolmogorov equation on the one-dimensional domain \((0,\pi)\) with Dirichlet or periodic boundary conditions. The novelty of this paper is that, based on a new method called attractor bifurcation, we investigate the existence of an attractor bifurcated from the trivial solution and give an explicit description of the bifurcated attractor. Moreover, the stability of the bifurcated branches is discussed.

MSC:

35B41 Attractors
35B32 Bifurcations in context of PDEs
35K20 Initial-boundary value problems for second-order parabolic equations
35K58 Semilinear parabolic equations
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