Almost mixed semi-continuous perturbation of Moreau's sweeping process

Doria Affane; Meriem Aissous; Mustapha Fateh Yarou

doi:10.3934/eect.2020015

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2020, Volume 9, Issue 1: 27-38. Doi: 10.3934/eect.2020015

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Almost mixed semi-continuous perturbation of Moreau's sweeping process

LMPA Laboratory, Department of Mathematics, Jijel University, 18000, Algeria

^* Corresponding author: Doria Affane
^* Corresponding author: Doria Affane

Received: April 30, 2018

Revised: July 31, 2019

Early access: October 2019

Published: March 2020

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Abstract

In this work, we introduce a new concept of semi-continuous set-valued mappings, called almost mixed semi-continuity, by taking maps that are upper semi-continuous with almost convex values in some points and lower semi-continuous in remaining points. We generalize earlier results obtained for both mixed semi-continuous maps and almost convex sets. We discuss the existence of solution for evolution problems driven by the so-called sweeping process subject to external forces, known as perturbation to the system, by this type of set-valued mappings. Finally, we give some topological properties of the attainable and solution sets in order to solve an optimal time problem.

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Mathematics Subject Classification: Primary: 34A60, 49J53; Secondary: 49J15.

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References

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