Representation formulas and large time behavior for solutions to some nonconvex Hamilton-Jacobi equations

TL;DR

This paper introduces a new representation formula for solutions to certain nonconvex Hamilton-Jacobi equations and analyzes their long-term behavior under specific conditions.

Contribution

It provides a novel representation formula for nonconvex Hamilton-Jacobi equations and studies their large time asymptotics.

Findings

New representation formula for solutions

Large time behavior established under additional assumptions

Applications demonstrated in periodic setting

Abstract

We give a new representation formula for solutions to nonconvex first-order Hamilton--Jacobi equations in the periodic setting and present some applications. We then prove the large time behavior for solutions under some additional assumptions.