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

Carvalho, A.; Langa, J.; Robinson, J.

doi:10.1090/S0002-9939-2011-11071-2

Structure and bifurcation of pullback attractors in a non-autonomous Chafee-Infante equation
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by A. N. Carvalho, J. A. Langa and J. C. Robinson PDF

Proc. Amer. Math. Soc. 140 (2012), 2357-2373 Request permission

Abstract:

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, $u_t=u_{xx}+\lambda u-\beta (t)u^3$, and investigate the bifurcations that this attractor undergoes as $\lambda$ 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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