RT info:eu-repo/semantics/article
T1 Global and cocycle attractors for non-autonomous reaction-diffusion equations. The case of null upper Lyapunov exponent
A1 Caraballo Garrido, Tomás
A1 Langa Rosado, José Antonio
A1 Obaya, Rafael
A1 Sanz Gil, Ana María
K1 Non-autonomous dynamical systems
K1 Global and cocycle attractors
K1 Linear-dissipative PDEs
K1 Li–Yorke chaos in measure
K1 Non-autonomous bifurcation theory
AB In this paper we obtain a detailed description of the global and cocycle attractors for the skew-product semiflows induced by the mild solutions of a family of scalar linear-dissipative parabolic problems over a minimal and uniquely ergodic flow. We consider the case of null upper Lyapunov exponent for the linear part of the problem. Then, two different types of attractors can appear, depending on whether the linear equations have a bounded or an unbounded associated real cocycle. In the first case (e.g.in periodic equations), the structure of the attractor is simple, whereas in the second case (which occurs in aperiodic equations), the attractor is a pinched set with a complicated structure. We describe situations when the attractor is chaotic in measure in the sense of Li–Yorke. Besides, we obtain a non-autonomous discontinuous pitchfork bifurcation scenario for concave equations, applicable for instance to a linear-dissipative version of the Chafee–Infante equation.
PB Elservier
SN 0022-0396
YR 2018
FD 2018
LK http://uvadoc.uva.es/handle/10324/32030
UL http://uvadoc.uva.es/handle/10324/32030
LA eng
NO J. Differential Equations, Noviembre 2018, vol. 265, n. 9, 3914-3951
DS UVaDOC
RD 07-ago-2024