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

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