KAKEN — Research Projects | Researcher Number: 80609545

Search Results: 5 results / Researcher Number: 80609545

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1. Canonical mean curvature flow and its application to evolution problems

Research Project

Research Category	Grant-in-Aid for Scientific Research (A)
Review Section	Medium-sized Section 12:Analysis, applied mathematics, and related fields
Research Institution	Tokyo Institute of Technology
Principal Investigator	利根川吉廣東京工業大学, 理学院, 教授
Project Period (FY)	2023-04-01 – 2028-03-31Granted
Keywords	mean curvature flow / evolution problem / minimal surface / phase interface
Outline of Research at the Start	幾何学的測度論の枠組みで考えるBrakkeの平均曲率流に関して，研究代表者らはその存在定理を示す過程で，Brakkeの平均曲率流の中でも特に良い性質をもつ平均曲率流の弱解である，標準的平均曲率流の概念に至った.標準的平均曲率流の特徴付けや正則性理論，その特異点集合の解析，特異点を持つ極小曲面に対する ...

2. Construction of a new mathematical model of grain boundary motion and development in the theory of differential equations

Research Project

Research Category	Grant-in-Aid for Scientific Research (C)
Review Section	Basic Section 12020:Mathematical analysis-related
Research Institution	Nihon University
Principal Investigator	水野将司日本大学, 理工学部, 准教授
Project Period (FY)	2022-04-01 – 2027-03-31Granted
Keywords	結晶成長 / Fokker-Planck方程式 / Lojasiewics-Simon勾配不等式 / 差分法 / Fokker-Planck 方程式 / 動的境界条件 / 曲率流方程式
Outline of Research at the Start	結晶成長の数理モデルの数学解析は, 幾何学的変分問題との関係もあいまって, 様々な研究が進んでおり, 微分方程式の新たな解析手法が構築されてきた. しかし, 結晶粒界上の結晶格子方位のずれによる特異性や, 結晶粒界同士が交差する三重点における相互作用を数理モデルにとりこむこと, そしてそのモデルを数 ...
Outline of Annual Research Achievements	昨年度に引き続き，空間不均一な拡散性とエネルギー則をみたす非線形Fokker-Planck系に周期境界条件を課した問題の解の長時間挙動を解析した．拡散の効果をエントロピー消散法に組み込むことにより，ポテンシャルの凸性を仮定しなくても，ポテンシャルの2階導関数が下に有界であれば，空間次元の制約のもと， ...
Current Status of Research Progress	1: Research has progressed more than it was originally planned.

Research Products of this project	Int'l Joint Research (6 results) Journal Article (6 results, of which Int'l Joint Research: 6 results, Peer Reviewed: 6 results) Presentation (8 results, of which Int'l Joint Research: 4 results, Invited: 3 results) Remarks (1 results) Funded Workshop (1 results)

3. Mathematical analysis about misorientations and triple junctions effects on evolution of grain boundaries

Research Project

Research Category	Grant-in-Aid for Early-Career Scientists
Review Section	Basic Section 12020:Mathematical analysis-related
Research Institution	Nihon University
Principal Investigator	MIZUNO Masashi 日本大学, 理工学部, 准教授
Project Period (FY)	2018-04-01 – 2022-03-31Completed
Keywords	結晶成長 / 曲率流方程式 / 幾何学的変分問題 / Fokker-Planck方程式 / 結晶方位差 / 三重点
Outline of Final Research Achievements	I studied mathematical modeling related to grain boundary motion and its mathematical analysis. In particular, to understand the interaction between m ...

Research Products of this project	Int'l Joint Research (2 results) Journal Article (4 results, of which Int'l Joint Research: 3 results, Peer Reviewed: 4 results) Presentation (18 results, of which Int'l Joint Research: 6 results, Invited: 3 results) Remarks (4 results)

4. Boundary behavior of solutions of the mean curvature flow with boundary conditions and nonlinear degenerate parabolic equations

Research Project

Research Category	Grant-in-Aid for Young Scientists (B)
Research Field	Mathematical analysis
Research Institution	Nihon University
Principal Investigator	Mizuno Masashi 日本大学, 理工学部, 准教授
Project Period (FY)	2013-04-01 – 2016-03-31Completed
Keywords	境界挙動 / 平均曲率流方程式 / 幾何学的測度論 / 特異極限問題 / 非線形固有値問題 / 退化放物型方程式
Outline of Final Research Achievements	We study the singular limit problem for the Allen-Cahn equation with Neumann boundary conditions and prove that associated energy measure converges to ...

Research Products of this project	Journal Article (2 results, of which Open Access: 1 results, Acknowledgement Compliant: 2 results, Peer Reviewed: 1 results) Presentation (11 results, of which Int'l Joint Research: 3 results, Invited: 7 results) Remarks (3 results)

5. Variational analysis on dynamic geometric problems

Research Project

Research Category	Grant-in-Aid for Scientific Research (A)
Research Field	Mathematical analysis
Research Institution	Tokyo Institute of Technology (2015-2018) Hokkaido University (2013-2014)
Principal Investigator	TONEGAWA Yoshihiro 東京工業大学, 理学院, 教授
Project Period (FY)	2013-05-31 – 2018-03-31Completed
Keywords	平均曲率流 / 変分問題 / 極小曲面 / 幾何学的測度論 / 特異点 / 正則性 / 変分法
Outline of Final Research Achievements	We proved the basic existence and regularity theorems for the mean curvature flow considered in the framework of geometric measure theory which is cal ...

Research Products of this project	Journal Article (29 results, of which Int'l Joint Research: 8 results, Peer Reviewed: 25 results, Open Access: 7 results, Acknowledgement Compliant: 4 results) Presentation (57 results, of which Int'l Joint Research: 21 results, Invited: 51 results) Funded Workshop (1 results)