2024-03-28T15:46:12Zhttps://uvadoc.uva.es/oai/requestoai:uvadoc.uva.es:10324/401992021-11-22T12:15:28Zcom_10324_1176com_10324_931com_10324_894col_10324_1359
Weak topologies for Carathéodory differential equations: continuous dependence, exponential dichotomy and attractors
Longo, Iacopo Paolo
Novo, Sylvia
Obaya, Rafael
Non-autonomous Carathéodory differential equations, Linearized skew-product flow, Exponential dichotomy, Pullback and forward attractors
Producción Científica
We introduce new weak topologies and spaces of Carathéodory functions where the solutions of the ordinary differential equations depend continuously on the initial data and vector fields. The induced local skew-product flow is proved to be continuous, and a notion of linearized skew-product flow is provided. Two applications are shown. First, the propagation of the exponential dichotomy over the trajectories of the linearized skew-product flow and the structure of the dichotomy or Sacker–Sell spectrum. Second, how particular bounded absorbing sets for the process defined by a Carathéodory vector field f provide bounded pullback attractors for the processes with vector fields in the alpha-limit set, the omega-limitset or the whole hull of f. Conditions for the existence of a pullback or a global attractor for the skew-product semiflow, as well as application examples are also given.
MINECO/FEDER Grant MTM2015-66330-P
H2020-MSCA-ITN-2014 643073 CRITICS
2020-01-14T15:49:02Z
2020-01-14T15:49:02Z
2019
info:eu-repo/semantics/article
info:eu-repo/semantics/acceptedVersion
https://doi.org/10.1007/s10884-018-9710-y
Journal of Dynamics and Differential Equations 31 (2019), 1617-1651.
1040-7294
http://uvadoc.uva.es/handle/10324/40199
1617
31
1651
Weak Topologies for Carathéodory Differential Equations:Continuous Dependence, Exponential Dichotomy and Attractors
eng
https://link.springer.com/content/pdf/10.1007/s10884-018-9710-y.pdf
info:eu-repo/grantAgreement/EC/H2020/643073
info:eu-repo/semantics/openAccess
application/pdf
Springer