Optimal convergence rate for homogenization of convex Hamilton–Jacobi equations in the periodic spatial-temporal environment

Abstract

We study the optimal convergence rate for the homogenization problem of convex Hamilton–Jacobi equations when the Hamitonian is periodic with respect to spatial and time variables, and notably time-dependent. We prove a result similar to that of (Tran and Yu (2021)), which means the optimal convergence rate is also O ( ε ).