Hamilton-Jacobi equations with jumps: asymptotic stability

TL;DR

This paper investigates the asymptotic stability of solutions to Hamilton-Jacobi equations with jumps, focusing on how strong dissipativity of jump controls influences stability, using differentiable flow orbits to analyze the characteristic system.

Contribution

It introduces a stability analysis framework for Hamilton-Jacobi equations with jumps based on dissipativity and flow orbits, advancing understanding of their long-term behavior.

Findings

Stability depends on the dissipativity of jump control functions.

Differentiable flow orbits effectively describe the characteristic system.

Conditions for asymptotic stability are established.

Abstract

The asymptotic stability of a global solution satisfying Hamilton-Jacobi equations with jumps will be analyzed in dependence on the strong dissipativity of the jump control function and using orbits of the differentiable flows to describe the corresponding characteristic system.