<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>Along this paper, we study an evolution inclusion governed by the so-called sweeping process. The right side of the inclusion contains a set-valued perturbation, supposed to be the external forces exercised on the system. We prove existence and relaxation results under weak assumptions on the perturbation by taking a truncated Lipschitz condition. These perturbations have non-convex and unbounded values without any compactness condition; we just assume a linear growth assumption on the element of minimal norm. The approach is based on the construction of approximate solutions. The relaxation is obtained by proving the density of the solution set of the original problem in a closure of the solution set of the relaxed one.</p>
</abstract>

Along this paper, we study an evolution inclusion governed by the so-called sweeping process. The right side of the inclusion contains a set-valued perturbation, supposed to be the external forces exercised on the system. We prove existence and relaxation results under weak assumptions on the perturbation by taking a truncated Lipschitz condition. These perturbations have non-convex and unbounded values without any compactness condition; we just assume a linear growth assumption on the element of minimal norm. The approach is based on the construction of approximate solutions. The relaxation is obtained by proving the density of the solution set of the original problem in a closure of the solution set of the relaxed one.

Non-convex perturbation to evolution problems involving Moreau’s sweeping process

Laboratory of Pure and Applied Mathematics, Faculty of Exact Sciences and Computer

Annals of West University of Timisoara - Mathematics and Computer Science

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Along this paper, we study an evolution inclusion governed by the so-called sweeping process. The right side of the inclusion contains a set-valued...

Non-convex perturbation to evolution problems involving Moreau’s sweeping process

Published Online: Dec 01, 2023

Page range: 151 - 175

DOI: https://doi.org/10.2478/awutm-2023-0012

Keywords
Relaxation, set-valued perturbation, truncation, normal cone, unboundedness

© 2023 Nouha Boudjerida et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Non-convex perturbation to evolution problems involving Moreau’s sweeping process

Published Online: Dec 01, 2023

Page range: 151 - 175

DOI: https://doi.org/10.2478/awutm-2023-0012

KeywordsRelaxation, set-valued perturbation, truncation, normal cone, unboundedness

© 2023 Nouha Boudjerida et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
Relaxation, set-valued perturbation, truncation, normal cone, unboundedness