Solution Properties of Convex Sweeping Processes with Velocity Constraint

TL;DR

This paper investigates key properties of solutions to convex sweeping processes with velocity constraints, including sensitivity, boundedness, closedness, and convexity, complementing existing results on their existence and uniqueness.

Contribution

It provides a detailed analysis of solution properties such as sensitivity, boundedness, closedness, and convexity for convex sweeping processes with velocity constraints.

Findings

Solution sensitivity with respect to initial conditions analyzed

Boundedness and closedness of solution sets established

Convexity of the solution set demonstrated

Abstract

Some properties of solutions of convex sweeping processes with velocity constraints are studied in this paper. Namely, the solution sensitivity with respect to the initial value, the boundedness, the closedness, and the convexity of the solution set are discussed in detail. Our investigations complement the preceding ones on the solution existence and the solution uniqueness of convex sweeping processes with velocity constraints.