Stability properties and large time behavior of viscosity solutions of Hamilton-Jacobi equations on metric spaces

TL;DR

This paper studies the long-term behavior and stability of viscosity solutions to Hamilton-Jacobi equations on general metric spaces, providing insights into their asymptotic properties.

Contribution

It introduces new stability and large time behavior results for viscosity solutions on metric spaces, extending classical theory to more general settings.

Findings

Established stability of solutions over time

Characterized asymptotic behavior of solutions

Extended Hamilton-Jacobi theory to metric spaces

Abstract

We investigate asymptotic behaviors of a metric viscosity solution of a Hamilton-Jacobi equation defined on a general metric space in Gangbo-\'{S}wi\c{e}ch sense. Our results include general stability and large time behavior of the solution.