## Title data

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 p.

DOI: https://doi.org/10.15495/EPub_UBT_00007160

## Project information

Project financing: |
Andere Bayerische Forschungsallianz „BayFor“ Mathematical Institute at Tel Aviv “MINT”, Tel Aviv University, Israel |
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## Abstract in another language

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.

## Further data

Item Type: | Preprint, postprint |
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Additional notes: | 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 |

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: | 05 Aug 2023 21:00 |

Last Modified: | 07 Aug 2023 05:29 |

URI: | https://eref.uni-bayreuth.de/id/eprint/86520 |