Sweeping processes with prescribed behaviour on jumps

TL;DR

This paper introduces a generalized sweeping process framework with prescribed behavior at jump points, proving existence and uniqueness, and applies it to elastoplasticity models with BV moving sets.

Contribution

It extends sweeping process theory to include prescribed jump behaviors and non-right continuous BV moving sets, with proven existence and uniqueness.

Findings

Established a generalized formulation with jump behavior control

Proved existence and uniqueness theorems for the new formulation

Applied results to elastoplasticity models with BV moving sets

Abstract

We present a generalized formulation of sweeping process where the behaviour of the solution is prescribed at the jump points of the driving moving set. An existence and uniqueness theorem for such formulation is proved. As a consequence we derive a formulation and an existence/uniqueness theorem for sweeping processes driven by an arbitrary BV moving set, whose evolution is not necessarily right continuous. Applications to the play operator of elastoplasticity are also shown.