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Título: Global and cocycle attractors for non-autonomous reaction-diffusion equations. The case of null upper Lyapunov exponent
Autor: Caraballo Garrido, Tomás
Langa Rosado, José Antonio
Obaya García, Rafael
Sanz Gil, Ana María
Año del Documento: 2018
Editorial: Elservier
Documento Fuente: J. Differential Equations, Noviembre 2018, vol. 265, n. 9, 3914-3951
Resumen: 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.
Palabras Clave: Non-autonomous dynamical systems
Global and cocycle attractors
Linear-dissipative PDEs
Li–Yorke chaos in measure
Non-autonomous bifurcation theory
ISSN: 0022-0396
Revisión por Pares: SI
DOI: 10.1016/j.jde.2018.05.023
Patrocinador: info:eu-repo/grantAgreement/EC/H2020/643073
Patrocinador: MINECO / FEDER grant MTM2015-66330-P
MINECO / FEDER grant MTM2015-63723-P
info:eu-repo/grantAgreement/EC/H2020/643073
Junta de Andalucía Proyecto de Excelencia FQM-1492
Version del Editor: https://www.sciencedirect.com/science/article/pii/S0022039618303048
Idioma: eng
URI: http://uvadoc.uva.es/handle/10324/32030
Derechos: info:eu-repo/semantics/openAccess
Aparece en las colecciones:Documentos OpenAire(Open Access Infrastructure for Research in Europe)
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