Vanishing viscosity limits for space-time periodic Hamiltonian-Jacobi-Bellman equations

TL;DR

This paper investigates the behavior of solutions to space-time periodic Hamilton-Jacobi-Bellman equations as viscosity vanishes, focusing on cases where the Aubry set consists of hyperbolic periodic orbits, extending previous results.

Contribution

It extends existing results on vanishing viscosity limits by considering cases with hyperbolic periodic orbits in the Aubry set, providing new insights into the structure of solutions.

Findings

Established convergence of solutions in the hyperbolic Aubry set case

Extended previous vanishing viscosity results to more complex Aubry set configurations

Provided a framework for analyzing Hamilton-Jacobi-Bellman equations with periodic structures

Abstract

Extending previuos results, we study the vanishing viscosity limit of solutions of space-time periodic Hamiltonian-Jacobi-Belllman equations, assuming that the "Aubry set" is the union of a finite number of hyperbolic periodic orbits of the Hamiltonian flow.