Flow Invariance on Stratified Domains

TL;DR

This paper develops Hamiltonian-based conditions to determine when trajectories of dynamical systems on stratified domains remain invariant, introducing the essential velocity multifunction to handle non-Lipschitz data.

Contribution

It introduces the essential velocity multifunction and establishes new invariance criteria for systems with non-Lipschitz data on stratified domains.

Findings

Hamiltonian conditions for weak invariance

Hamiltonian conditions for strong invariance

Properties of the essential velocity multifunction

Abstract

This paper studies conditions for invariance of dynamical systems on stratified do- mains as originally introduced by Bressan and Hong. We establish Hamiltonian conditions for both weak and strong invariance of trajectories on systems with non-Lipschitz data. This is done via the identification of a new multifunction, the essential velocity multifunction. Properties of this multifunction are investigated and used to establish the relevant invariance criteria.