Title data
Baier, Robert ; Farkhi, Elza:
A Filippov Approximation Theorem for Strengthened OneSided Lipschitz Differential Inclusions.
In: Computational Optimization and Applications.
(11 September 2023)
.
 pp. 139.
ISSN 09266003
DOI: https://doi.org/10.1007/s10589023005179
This is the latest version of this item.
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Project information
Project financing: 
Andere Bayerische Forschungsallianz „BayFor“ Mathematical Institute at Tel Aviv “MINT”, Tel Aviv University, Israel 

Abstract in another language
We consider differential inclusions with strengthened onesided Lipschitz (SOSL) righthand sides. The class of SOSL multivalued maps is wider than the class of Lipschitz ones and a subclass of the class of onesided Lipschitz maps. We prove a Filippov approximation theorem for the solutions of such differential inclusions with perturbations in the righthand 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 onesided Lipschitz (OSL) righthand sides from 1/2 to 1.
Further data
Item Type:  Article in a journal 

Refereed:  Yes 
Additional notes:  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 setvalued maps 3. Filippovtype 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 righthand side Conclusions 
Keywords:  differential inclusions; Filippov theorem; (strengthened) onesided Lipschitz condition; monotonicity; setvalued Euler method; reachable sets 
Subject classification:  Mathematics Subject Classification Code: 47H05, 47H06, 54C60 (26E25, 34A60, 34A36, 49M25) 
Institutions of the University:  Faculties Faculties > Faculty of Mathematics, Physics und Computer Science Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematics V (Applied Mathematics) Profile Fields Profile Fields > Advanced Fields Profile Fields > Advanced Fields > Nonlinear Dynamics Research Institutions > Central research institutes > Bayreuth Research Center for Modeling and Simulation  MODUS Research Institutions Research Institutions > Central research institutes 
Result of work at the UBT:  Yes 
DDC Subjects:  500 Science > 510 Mathematics 
Date Deposited:  25 Oct 2023 08:41 
Last Modified:  25 Oct 2023 08:41 
URI:  https://eref.unibayreuth.de/id/eprint/87380 
Available Versions of this Item

A Filippov Approximation Theorem for Strengthened OneSided Lipschitz Differential Inclusions. (deposited 05 Aug 2023 21:00)

A Filippov Approximation Theorem for Strengthened OneSided Lipschitz Differential Inclusions. (deposited 12 Oct 2023 09:07)
 A Filippov Approximation Theorem for Strengthened OneSided Lipschitz Differential Inclusions. (deposited 25 Oct 2023 08:41) [Currently Displayed]

A Filippov Approximation Theorem for Strengthened OneSided Lipschitz Differential Inclusions. (deposited 12 Oct 2023 09:07)