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Baier, Robert ; Farkhi, Elza:
A Filippov Approximation Theorem for Strengthened One-Sided Lipschitz Differential Inclusions.
Mathematisches Institut, Universität Bayreuth; School of Mathematical Sciences, Tel Aviv University
Bayreuth ; Tel Aviv
,
2023
. - 31 S.
DOI: https://doi.org/10.15495/EPub_UBT_00007160
Volltext
Angaben zu Projekten
| 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 stability 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 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.
Weitere Angaben
| Publikationsform: | Preprint, Postprint |
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| Zusätzliche Informationen: | accepted for publication in a special issue in the journal “Computational Optimization and Applications” in memory of Asen Dontchev 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 boundednes 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: | 05 Aug 2023 21:00 |
| Letzte Änderung: | 16 Okt 2023 05:53 |
| URI: | https://eref.uni-bayreuth.de/id/eprint/86520 |
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