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arXiv · 2303.02923

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

Hiroyoshi Mitake·Shoichi Sato
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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.

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Hiroyoshi Mitake, Shoichi Sato. 2023-03-06. On the rate of convergence in homogenization of time-fractional Hamilton-Jacobi equations. https://arxiv.org/abs/2303.02923

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