2023-03-31T12:37:57Zhttps://uvadoc.uva.es/oai/requestoai:uvadoc.uva.es:10324/320302021-06-24T07:41:03Zcom_10324_32197com_10324_952com_10324_894com_10324_1145com_10324_931col_10324_32199col_10324_1254
Global and cocycle attractors for non-autonomous reaction-diffusion equations. The case of null upper Lyapunov exponent
Caraballo Garrido, Tomás
Langa Rosado, José Antonio
Obaya García, Rafael
Sanz Gil, Ana María
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.
2018-10-08T13:05:04Z
2018-10-08T13:05:04Z
2018-10-08T13:05:04Z
2018
info:eu-repo/semantics/article
J. Differential Equations, Noviembre 2018, vol. 265, n. 9, 3914-3951
0022-0396
http://uvadoc.uva.es/handle/10324/32030
10.1016/j.jde.2018.05.023
3914
265
3951
eng
https://www.sciencedirect.com/science/article/pii/S0022039618303048
info:eu-repo/grantAgreement/EC/H2020/643073
info:eu-repo/semantics/openAccess
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