On the rate of convergence in homogenization of time-fractional Hamilton-Jacobi equations

Abstract

Here, we consider periodic homogenization for time-fractional Hamilton-Jacobi equations. By using the perturbed test function method, we establish the convergence, and give estimates on a rate of convergence. A main difficulty is the incompatibility between the function used in the doubling variable method, and the non-locality of the Caputo derivative. Our approach is to provide a lemma to prove the rate of convergence without the doubling variable method with respect to the time variable, which is a key ingredient.

Rate of convergence in periodic homogenization for convex Hamilton–Jacobi equations with multiscales

“…Additionally, the optimal rate of O(ϵ) was obtained in [9] for convex Hamiltonians H = H(y, s, p) that also depend periodically on the time variable. For a recent study on the rate of convergence for timefractional Hamilton-Jacobi equations with Caputo fractional derivatives, see [7]. We refer the reader to [2,8,11] for further references therein.…”

Rate of Convergence in Periodic Homogenization for Convex Hamilton-Jacobi Equations with Multiscales

“…Additionally, the optimal rate of O(ǫ) was obtained in [8] for convex Hamiltonians H = H(y, s, p) that also depend periodically on the time variable. For a recent study on the rate of convergence for time-fractional Hamilton-Jacobi equations with Caputo fractional derivatives, see [6]. We refer the reader to [2,7,10] for further references therein.…”