Rate of convergence for homogenization of nonlinear weakly coupled Hamilton-Jacobi systems

TL;DR

This paper investigates the homogenization process for nonlinear weakly coupled Hamilton-Jacobi systems, establishing a sharp convergence rate of O(√ε) in a convex setting, advancing understanding of their asymptotic behavior.

Contribution

The paper provides the first sharp rate of convergence for homogenization of nonlinear weakly coupled Hamilton-Jacobi systems in the convex case.

Findings

Established a convergence rate of O(√ε) for the homogenization process.

Proved the sharpness of the convergence rate.

Extended homogenization results to nonlinear weakly coupled systems.

Abstract

Here, we study the periodic homogenization problem of nonlinear weakly coupled systems of Hamilton-Jacobi equations in the convex setting. We establish a rate of convergence $O(\sqrt{\varepsilon})$ which is sharp.