Projection process with definable right-hand side

TL;DR

This paper explores the connection between sweeping processes and projection processes within definable sets, proving solution existence under certain conditions and applying it to a crowd motion model.

Contribution

It establishes the existence of solutions for perturbed sweeping and projection processes in definable sets within o-minimal structures, extending previous results.

Findings

Proved existence of solutions for perturbed sweeping processes.

Extended solution existence to nonstationary projection processes.

Applied theoretical results to a crowd motion model.

Abstract

We study the relation between sweeping processes with the cone of limiting normals and projection processes. We prove the existence of solution of a perturbed sweeping process with the cone of limiting normals and of nonstationary projection process, provided the sets involved are definable (and are moving in a definable way) in some o-minimal structure. An application to a crowd motion model is presented.