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Takashi Kagaya, Global stability of traveling waves for an area preserving curvature flow with contact angle condition, *Journal of Differential Equations*, 2020.03. |

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Takashi Kagaya, Yoshihito Kohsaka, Existence of non-convex traveling waves for surface diffusion of curves with constant contact angles, *Arch. Ration. Mech. Anal.*, https://doi.org/10.1007/s00205-019-01426-0, 2019.07, The traveling waves for surface diffusion of plane curve are studied. We cosigner an evolving plane curve with two endpoints which can move freely on the x-axis with generating constant contact angles. For the evolution of this plane curve governed by surface diffusion, we discuss the existence, the uniqueness and the convexity of traveling waves. The main results show that the uniqueness and the convexity can be lost depending on the conditions of the contact angles, although the existence holds for any contact angles in the interval (0, π/2).. |

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Takashi Kagaya, Convergence of the Allen-Cahn equation with a zero Neumann boundary condition on non-convex domains, *Math. Ann.*, 10.1007/s00208-018-1720-x, 373, 3, 1485-1528, 2019.03, We study a singular limit problem of the Allen-Cahn equation with a homogeneous Neumann boundary condition on non-convex domains with smooth boundaries under suitable as- sumptions for initial data. The main result is the convergence of the time parametrized family of the diffused surface energy to Brakke’s mean curvature flow with a generalized right angle condition on the boundary of the domain.. |

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Takashi Kagaya, Yoshihiro Tonegawa, A singular perturbation limit of diffused interface energy with a fixed contact angle condition, *Indiana University Math. J.*, 10.1512/iumj.2018.67.7423, 67, 4, 1425-1437, 2018.01, 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 that the limit varifold derived from the diffused energy satisfies a generalized contact angle condition on the boundary under a set of assumptions.. |

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Takashi Kagaya, Yoshihiro Tonegawa, A fixed contact angle condition for varifolds, *Hiroshima Math. J.*, 0018-2079, 47, 2, 139-153, 2017.07, We define a generalized fixed contact angle condition for n-varifold and establish a boundary monotonicity formula. The results are natural generalizations of those for the Neumann boundary condition considered by Gru ̈ter-Jost.. |

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Takashi Kagaya, Masahiko Shimojo, Exponential stability of a traveling wave for an area preserving curvature motion with two endpoints moving freely on a line, *Asymptotic Analysis*, 10.3233/ASY-151335, 96, 2, 109-134, 2016.04, The asymptotic behavior of solutions to an area-preserving curvature flow of planar curves in the upper half plane is investigated. Two endpoints of the curve slide along the horizontal axis with prescribed fixed contact angles. First, by es- tablishing an isoperimetric inequality, we prove the global existence of the solution. We then study the asymptotic behavior of solutions with concave initial data near a traveling wave.. |