Commutation Properties of Semi-groups for Contact Type Hamilton-Jacobi Equation

TL;DR

This paper proves the commutation properties of semi-groups associated with contact type Hamilton-Jacobi equations, extending known results from classical Hamilton-Jacobi equations to the contact case.

Contribution

It provides a new proof of the commutation property for semi-groups in contact type Hamilton-Jacobi equations, which was previously unestablished.

Findings

Established the commutation property for semi-groups in contact Hamilton-Jacobi equations

Extended classical results to the contact case

Provided a rigorous proof of the property

Abstract

We know that there exist semi-groups for contact type Hamilton-Jacobi equations, which refers to \cite{KLJ2}. Guy Barles and Agn\`es Tourin give a proof of the commutation properties for normal Hamilton-Jacobi equations at \cite{GA}. In this article, we provide a proof of the commutation property of semi-groups for contact type Hamilton-Jacobi equations.