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Baier, Robert ; Farkhi, Elza:
A Filippov Approximation Theorem for Strengthened One-Sided Lipschitz Differential Inclusions.
In: Computational Optimization and Applications.
(11 September 2023)
.
- S. 1-39.
ISSN 0926-6003
DOI: https://doi.org/10.1007/s10589-023-00517-9
Dies ist die aktuelle Version des Eintrags.
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| Projektfinanzierung: |
Andere Bayerische Forschungsallianz „BayFor“ Mathematical Institute at Tel Aviv “MINT”, Tel Aviv University, Israel |
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Abstract
We consider differential inclusions with strengthened one-sided Lipschitz (SOSL) right-hand sides. The class of SOSL multivalued maps is wider than the class of Lipschitz ones and a subclass of the class of one-sided Lipschitz maps. We prove a Filippov approximation theorem for the solutions of such differential inclusions with perturbations in the right-hand side, both of the set of the velocities (outer perturbations) and of the state (inner perturbations). The obtained estimate of the distance between the approximate and exact solution extends the known Filippov estimate for Lipschitz maps to SOSL ones and improves the order of approximation with respect to the inner perturbation known for one-sided Lipschitz (OSL) right-hand sides from 1/2 to 1.
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| Publikationsform: | Artikel in einer Zeitschrift |
|---|---|
| Begutachteter Beitrag: | Ja |
| Zusätzliche Informationen: | special issue in memory of Asen Dontchev (Open Access)
Contents: 1. Introduction 2. Preliminaries and examples 2.1 Notation 2.2 Inner and outer perturbations 2.3 Examples for SOSL/OSL set-valued maps 3. Filippov-type theorems for SOSL maps 3.1 Existence and boundedness of solutions 3.2 Filippov approximation theorem for the SOSL case 3.3 Stability and approximation results 4 Examples of differential inclusions with SOSL right-hand side Conclusions |
| Keywords: | differential inclusions; Filippov theorem; (strengthened) one-sided Lipschitz condition; monotonicity; set-valued Euler method; reachable sets |
| Fachklassifikationen: | Mathematics Subject Classification Code: 47H05, 47H06, 54C60 (26E25, 34A60, 34A36, 49M25) |
| Institutionen der Universität: | Fakultäten Fakultäten > Fakultät für Mathematik, Physik und Informatik Fakultäten > Fakultät für Mathematik, Physik und Informatik > Mathematisches Institut Fakultäten > Fakultät für Mathematik, Physik und Informatik > Mathematisches Institut > Lehrstuhl Mathematik V (Angewandte Mathematik) Profilfelder Profilfelder > Advanced Fields Profilfelder > Advanced Fields > Nichtlineare Dynamik Forschungseinrichtungen > Zentrale wissenschaftliche Einrichtungen > Bayreuther Zentrum für Modellierung und Simulation (MODUS) Forschungseinrichtungen Forschungseinrichtungen > Zentrale wissenschaftliche Einrichtungen |
| Titel an der UBT entstanden: | Ja |
| Themengebiete aus DDC: | 500 Naturwissenschaften und Mathematik > 510 Mathematik |
| Eingestellt am: | 25 Okt 2023 08:41 |
| Letzte Änderung: | 25 Okt 2023 08:41 |
| URI: | https://eref.uni-bayreuth.de/id/eprint/87380 |
Zu diesem Eintrag verfügbare Versionen
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A Filippov Approximation Theorem for Strengthened One-Sided Lipschitz Differential Inclusions. (deposited 05 Aug 2023 21:00)
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A Filippov Approximation Theorem for Strengthened One-Sided Lipschitz Differential Inclusions. (deposited 12 Okt 2023 09:07)
- A Filippov Approximation Theorem for Strengthened One-Sided Lipschitz Differential Inclusions. (deposited 25 Okt 2023 08:41) [Aktuelle Anzeige]
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A Filippov Approximation Theorem for Strengthened One-Sided Lipschitz Differential Inclusions. (deposited 12 Okt 2023 09:07)