Affiliation:
1. Faculty of Mathematics and Computer Science, University of Science, Vietnam National University Ho Chi Minh City, Vietnam
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 ).
Reference9 articles.
1. Periodic metrics;Burago;Adv. Soviet Math.,1992
2. On the rate of convergence in homogenization of Hamilton–Jacobi equations;Capuzzo-Dolcetta;Indiana Univ. Math. J.,2001
3. A near-optimal rate of periodic homogenization for convex Hamilton–Jacobi equations;Cooperman;Arch. Ration. Mech. Anal.,2022
4. M. Einseidler and T. Ward, Functional Analysis, Spectral Theory, and Applications, Graduate Texts in Mathematics, Vol. 276, Springer International Publishing AG, 2017.
5. Effective Hamiltonians and averaging for Hamiltonian dynamics II;Evans;Arch. Ration. Mech. Anal.,2002