Artículo
Global and cocycle attractors for non-autonomous reaction-diffusion equations. The case of null upper Lyapunov exponent
Autor/es | Caraballo Garrido, Tomás
Langa Rosado, José Antonio Obaya García, Rafael Sanz Gil, Ana María |
Departamento | Universidad de Sevilla. Departamento de Ecuaciones Diferenciales y Análisis Numérico |
Fecha de publicación | 2018-11-05 |
Fecha de depósito | 2018-09-12 |
Publicado en |
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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 ... 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, basically two different types of attractors can appear, depending on whether the linear coefficient in the equations determines a bounded or an unbounded associated real cocycle. In the first case (the one for periodic equations), the structure of the attractor is simple, whereas in the second case (which happens in aperiodic equations), the attractor is a pinched set with a complicated structure. We describe situations in which 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. |
Identificador del proyecto | MTM2015-66330
H2020-MSCA-ITN-2014 643073 CRITICS FQM-1492 MTM2015- 63723-P |
Cita | Caraballo Garrido, T., Langa Rosado, J.A., Obaya García, R. y Sanz Gil, A.M. (2018). Global and cocycle attractors for non-autonomous reaction-diffusion equations. The case of null upper Lyapunov exponent. Journal of Differential Equations, 265 (9), 3914-3951. |
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