Monotone Multivalued Nonautonomous Dynamical Systems
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866916310448865280 |
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| author | Langa, José A. Simsen, Jacson Simsen, Mariza Stefanello Valero, José |
| author_facet | Langa, José A. Simsen, Jacson Simsen, Mariza Stefanello Valero, José |
| contents | This paper is devoted to the study of nonautonomous multivalued semiflows and their associated pullback attractors. For this kind of dynamical systems we are able to characterize the upper and lower bounds of the attractor as complete trajectories belonging to the attractor, so that all the internal dynamics is confined in this region, which can be described as an interval due to the orderly nature of the processes. Thus, we are able to generalize to this framework previous general results in literature for autonomous multivalued flows or nonautonomous differential equations. We apply our results to a partial differential inclusion with a nonautonomous term, also proving the upper semicontinuity dependence of pullback and global attractors when the time dependent term asymptotically converges to an autonomous multivalued term. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_02851 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Monotone Multivalued Nonautonomous Dynamical Systems Langa, José A. Simsen, Jacson Simsen, Mariza Stefanello Valero, José Dynamical Systems 35B40, 35B41, 35B51, 35K55, 35K57 This paper is devoted to the study of nonautonomous multivalued semiflows and their associated pullback attractors. For this kind of dynamical systems we are able to characterize the upper and lower bounds of the attractor as complete trajectories belonging to the attractor, so that all the internal dynamics is confined in this region, which can be described as an interval due to the orderly nature of the processes. Thus, we are able to generalize to this framework previous general results in literature for autonomous multivalued flows or nonautonomous differential equations. We apply our results to a partial differential inclusion with a nonautonomous term, also proving the upper semicontinuity dependence of pullback and global attractors when the time dependent term asymptotically converges to an autonomous multivalued term. |
| title | Monotone Multivalued Nonautonomous Dynamical Systems |
| topic | Dynamical Systems 35B40, 35B41, 35B51, 35K55, 35K57 |
| url | https://arxiv.org/abs/2407.02851 |