22 citations · 40 across the 10 of their papers we have counts for
10 papers
Singular Dirichlet boundary problems for a class of fully nonlinear parabolic equations in one dimension
Takashi Kagaya
In this paper, we deal with the initial value problem for a class of fully nonlinear parabolic equations with a singular Dirichlet boundary condition in one space dimension. The in…
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…
Quasiconvexity preserving property for fully nonlinear nonlocal parabolic equations
Takashi Kagaya, Qing Liu, Hiroyoshi Mitake
This paper is concerned with a general class of fully nonlinear parabolic equations with monotone nonlocal terms. We investigate the quasiconvexity preserving property of positive,…
Long time behavior for a curvature flow of networks related to grain bundary motion with the effect of lattice misorientations
Takashi Kagaya, Masashi Mizuno, Keisuke Takasao
The mathematical model of grain boundary motion, including lattice misorientations' effect, is considered. When time-dependent lattice misorientations are state variables of the su…
Singular Neumann boundary problems for a class of fully nonlinear parabolic equations in one dimension
Takashi Kagaya, Qing Liu
In this paper, we discuss singular Neumann boundary problem for a class of nonlinear parabolic equations in one space dimension. Our boundary problem describes motion of a planar c…
Global stability of traveling waves for an area preserving curvature flow with contact angle condition
Takashi Kagaya
We consider an evolving plane curve with two endpoints that can move freely on the -axis with generating constant contact angles. We discuss the asymptotic behavior of global-in…
Existence of non-convex traveling waves for surface diffusion of curves with constant contact angles
Takashi Kagaya, Yoshihito Kohsaka
The traveling waves for surface diffusion of plane curves are studied. We consider an evolving plane curve with two endpoints, which can move freely on the x-axis with generating c…
Convergence of the Allen-Cahn equation with a zero Neumann boundary condition on non-convex domains
Takashi Kagaya
We study a singular limit problem of the Allen-Cahn equation with the homogeneous Neumann boundary condition on non-convex domains with smooth boundaries under suitable assumptions…
A singular perturbation limit of diffused interface energy with a fixed contact angle condition
Takashi Kagaya, Yoshihiro Tonegawa
We study a general asymptotic behavior of critical points of a diffused interface energy with a fixed contact angle condition defined on a domain . We show t…
A fixed contact angle condition for varifolds
Takashi Kagaya, Yoshihiro Tonegawa
We define a generalized fixed contact angle condition for -varifold and establish a boundary monotonicity formula. The results are natural generalizations of those for the Neuma…