Viability and Exponentially Stable Trajectories for Differential Inclusions in Wasserstein Spaces

TL;DR

This paper establishes a viability theorem for differential inclusions in Wasserstein spaces and demonstrates the existence of exponentially stable trajectories using Lyapunov methods, advancing the understanding of stability in measure spaces.

Contribution

It introduces a general viability theorem for continuity inclusions in Wasserstein spaces and applies Lyapunov methods to prove the existence of exponentially stable trajectories.

Findings

Proved a viability theorem for continuity inclusions in Wasserstein spaces.

Established the existence of exponentially stable trajectories.

Applied Lyapunov methods to measure space dynamics.

Abstract

In this article, we prove a general viability theorem for continuity inclusions in Wasserstein spaces, and provide an application thereof to the existence of exponentially stable trajectories obtained via the second method of Lyapunov.