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Takashi Kagaya Last modified date:2019.06.17





Academic Degree
Doctor of Science
Field of Specialization
Partial Differential Equation
Outline Activities
The subjects of my research are variational problems for surfaces and surface evolution equations. In particular, I am interested in the mathematical structure of the contact angle between two surfaces, so my recent researches are analysis for surface evolution equations with contact angle conditions and characterization of surfaces with contact angles by using an energy functional which appeared in a phase separation model. On these researches, I apply analysis of the asymptotic behavior of classical solutions (smooth solutions) and the geometric measure theory which enable representation of a surface with singularities as a measure.
Research
Research Interests
  • Surfaces with contact angle structure
    keyword : Surface evolution equation, Contact angle, Geometric measure theory, Variational problems
    2013.04~2023.05.
Academic Activities
Papers
1. 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..
2. 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..
3. 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..
4. 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..
Membership in Academic Society
  • The Mathematical Society of Japan