Structure and bifurcation of pullback attractors in a non-autonomous Chafee-Infante equation

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Carvalho, Alexandre Nolasco de ; Langa, José A. ; Robinson, James C. (2012)

The Chafee-Infante equation is one of the canonical infinite-dimensional dynamical systems for which a complete description of the global attractor is available. In this paper we study the structure of the pullback attractor for a non-autonomous version of this equation, ut = uxx + λu - β(t)u3, and investigate the bifurcations that this attractor undergoes as λ is varied. We are able to describe these in some detail, despite the fact that our model is truly non-autonomous; i.e., we do not restrict to 'small perturbations' of the autonomous case.
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