Geometrical analysis study on interface dynamics with contact angle structure

2023 Fiscal Year Final Research Report

• Project/Area Number: 19K14572
• Research Category: Grant-in-Aid for Early-Career Scientists
• Allocation Type: Multi-year Fund
• Review Section: Basic Section 12020:Mathematical analysis-related
• Research Institution: Muroran Institute of Technology (2021-2023); Kyushu University (2019-2020)
• Principal Investigator: Kagaya Takashi 室蘭工業大学, 大学院工学研究科, 准教授 (60814431)
• Project Period (FY): 2019-04-01 – 2024-03-31
• Keywords: 曲面の発展方程式 / 接触角条件 / 偏微分方程式

Outline of Final Research Achievements

(1) Solvability and asymptotic behavior analysis of initial value problems are studied for an area-conserving curvature flow with contact angle conditions, an interface rising model with tangential boundary condition, and network solutions with crystal particle orientation parameters. These include joint works with Qing Liu (Okinawa Institute of Science and Technology), Keisuke Takasao (Kyoto University), and Masashi Mizuno (Nihon University).
(2) For the equation described by the level set formulation of geometric flow with a nonlocal term, where the normal velocity depends on the volume enclosed by the curved surface, the results of convexity conservation of solutions, an expression formula of solutions, and the asymptotic behavior analysis of solutions using the formula are studied. These are joint works with Qing Liu (Okinawa Institute of Science and Technology) and Hiroyoshi Mitake (The University of Tokyo).

Free Research Field

曲面の発展方程式

Academic Significance and Societal Importance of the Research Achievements

本研究課題の成果のうち，学術的な特徴として，以下の項目が挙げられる．（１）有界な曲線の挙動においては，接触角条件によっては，進行波解が安定性を持ち，これは境界条件を課さない閉曲線に対する挙動においては見られない現象である．（２）界面現象モデルにおいて，接的な境界条件を満たす解の可解性は方程式の構造に依存し，これは既存の結果における，接触角条件を課した場合と異なる構造である．これらの研究成果は，境界条件によって異なる構造が現れることを解明しているため，本研究課題の学術的意義となる．また，社会的意義は，本研究課題で扱っているモデルは，物理的背景を伴うことが挙げられる．