48 citations · 152 across the 34 of their papers we have counts for
38 papers
Quantitative homogenization of state-constraint Hamilton--Jacobi equations on perforated domains and applications
Yuxi Han, Wenjia Jing, Hiroyoshi Mitake +1
We study the periodic homogenization problem of state-constraint Hamilton--Jacobi equations on perforated domains in the convex setting and obtain the optimal convergence rate. We…
Quenching for axisymmetric hypersurfaces under forced mean curvature flows
Hiroyoshi Mitake, Yusuke Oka, Hung Vinh Tran
Here, we study the motion of axisymmetric hypersurfaces evolved by forced mean curvature flows in the periodic setting. We establish conditions that quenching occ…
Asymptotic growth rate of solutions to level-set forced mean curvature flows with evolving spirals
Hiroyoshi Mitake, Hung V. Tran
Here, we study a level-set forced mean curvature flow with evolving spirals and the homogeneous Neumann boundary condition, which appears in a crystal growth model. Under some appr…
A representation formula for viscosity solutions of nonlocal Hamilton--Jacobi equations and applications
Takashi Kagaya, Qing Liu, Hiroyoshi Mitake
This paper is concerned with geometric motion of a closed surface whose velocity depends on a nonlocal quantity of the enclosed region. Using the level set formulation, we study a…
A level-set method for a mean curvature flow with a prescribed boundary
Xingzhi Bian, Yoshikazu Giga, Hiroyoshi Mitake
We propose a level-set method for a mean curvature flow whose boundary is prescribed by interpreting the boundary as an obstacle. Since the corresponding obstacle problem is global…
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…