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math.AP2023
On the rate of convergence in homogenization of time-fractional Hamilton-Jacobi equations
Hiroyoshi Mitake, Shoichi Sato
Here, we consider periodic homogenization for time-fractional Hamilton--Jacobi equations. By using the perturbed test function method, we establish the convergence, and give estima…
math.AP2021
On the equivalence of viscosity solutions and distributional solutions for the time-fractional diffusion equation
Yoshikazu Giga, Hiroyoshi Mitake, Shoichi Sato
We consider an initial-boundary value problem for the time-fractional diffusion equation. We prove the equivalence of two notions of weak solutions, viscosity solutions and distrib…