7 citations · 13 across the 8 of their papers we have counts for
8 papers · 1 filter
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…
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…
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…
Weak KAM theory for discount Hamilton-Jacobi equations and its application
Hiroyoshi Mitake, Kohei Soga
Weak KAM theory for discount Hamilton-Jacobi equations and corresponding discount Lagrangian/Hamiltonian dynamics is developed. Then it is applied to error estimates for viscosity…
Selection problems for a discounted degenerate viscous Hamilton--Jacobi equation
Hiroyoshi Mitake, Hung V. Tran
We prove that the solution of the discounted approximation of a degenerate viscous Hamilton--Jacobi equation with convex Hamiltonians converges to that of the associated ergodic pr…
Existence for stationary mean field games with quadratic Hamiltonians with congestion
Diogo A. Gomes, Hiroyoshi Mitake
In this paper, we investigate the existence and uniqueness of solutions to a stationary mean field game model introduced by J.-M. Lasry and P.-L. Lions. This model features a quadr…