On the vanishing contact structure for viscosity solutions of contact type Hamilton-Jacobi equations I: Cauchy problem

TL;DR

This paper investigates the fundamental and viscosity solutions of contact type Hamilton-Jacobi equations, providing representation formulas and a vanishing contact structure result that extends the vanishing discount problem.

Contribution

It introduces new representation formulas for solutions and extends the vanishing discount problem to contact type Hamilton-Jacobi equations.

Findings

Derived representation formulas for fundamental and viscosity solutions.

Established a vanishing contact structure result for Cauchy problems.

Extended the vanishing discount problem to contact Hamilton-Jacobi equations.

Abstract

We study the representation formulae for the fundamental solutions and viscosity solutions of the Hamilton-Jacobi equations of contact type. We also obtain a vanishing contact structure result for relevant Cauchy problems which can be regarded as an extension to the vanishing discount problem.