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

Article type: Research Article

Authors: Nguyen-Tien, Hoang^{; *}

Affiliations: Faculty of Mathematics and Computer Science, University of Science, Vietnam National University Ho Chi Minh City, Vietnam

Correspondence: [*] Corresponding author. E-mail: htnguyen35@wisc.edu.

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).

Keywords: Hamilton–Jacobi equations, homogenization, spatio-temporal periodic setting, optimal convergent rate, viscosity solutions

DOI: 10.3233/ASY-241898

Journal: Asymptotic Analysis, vol. 138, no. 1-2, pp. 135-150, 2024