RT info:eu-repo/semantics/article
T1 Weak topologies for Carathéodory differential equations: continuous dependence, exponential dichotomy and attractors
A1 Longo, Iacopo Paolo
A1 Novo, Sylvia
A1 Obaya, Rafael
K1 Non-autonomous Carathéodory differential equations, Linearized skew-product flow, Exponential dichotomy, Pullback and forward attractors
AB 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.
PB Springer
SN 1040-7294
YR 2019
FD 2019
LK http://uvadoc.uva.es/handle/10324/40199
UL http://uvadoc.uva.es/handle/10324/40199
LA eng
NO Journal of Dynamics and Differential Equations 31 (2019), 1617-1651.
NO Producción Científica
DS UVaDOC
RD 16-nov-2024