SEARCH

Search Details

Hamamuki Nao

Faculty of Science　Mathematics　MathematicsAssociate Professor
Research Center of Mathematics for Social CreativityAssociate Professor

Researcher basic information

■ Degree
  • Doctor of Philosophy in the field of Mathematical Sciences, The University of Tokyo
■ URL
researchmap URLホームページURL■ Various IDs
Researcher number
  • 70749754
J-Global ID■ Research Keywords and Fields
Research Keyword
  • Level set method
  • Nonlinear partial differential equations
  • Comparison principle
  • Hamilton-Jacobi equation
  • Viscosity solution
Research Field
  • Natural Science, Mathematical analysis, Nonlinear partial differential equations
■ Educational Organization

Career

■ Career
Career
  • Oct. 2016 - Present
    Hokkaido University, Department of Mathematics, Associate Professor
  • Feb. 2015 - Sep. 2016
    Hokkaido University, Department of Mathematics, Assistant Professor
  • Apr. 2014 - Jan. 2015
    Waseda University, Faculty of Education and Integrated Arts and Sciences, JSPS Research Fellowship PD
  • Oct. 2013 - Mar. 2014
    The University of Tokyo, Graduate School of Mathematical Sciences, JSPS Research Fellowship PD
Educational Background
  • Apr. 2009 - Sep. 2013, The University of Tokyo, Graduate School of Mathematical Sciences
  • Apr. 2005 - Mar. 2009, The University of Tokyo, Faculty of Science, Department of Mathematics

Research activity information

■ Awards
  • Feb. 2020, Hokkaido University, President's Award
    HAMAMUKI Nao
  • Feb. 2016, Inoue Foundation for Science, 32nd Inoue Research Award for Young Scientists
    HAMAMUKI Nao
  • Feb. 2014, Japan Society for the Promotion of Science, 4th Ikushi Prize
    Crystal Growth Phenomena and Hamilton-Jacobi Equations
    HAMAMUKI Nao
  • Sep. 2013, Mathematical Society of Japan, Takebe Katahiro Prize for Encouragement of Young Researchers
    Mathematical analysis for Hamilton-Jacobi equations and its application to crystal growth phenomena
    HAMAMUKI Nao
■ Papers
■ Lectures, oral presentations, etc.
  • 非凸な石の摩耗過程における待ち時間効果
    HAMAMUKI Nao
    談話会（東京理科大学）, Dec. 2024, Japanese, Public discourse
    [Invited]
  • Waiting time effects for the wearing process of a non-convex stone
    HAMAMUKI Nao
    Geometric PDE and Applied Analysis Seminar, Dec. 2023, English, Public discourse
    [Invited]
  • Waiting time effects for the wearing process of a non-convex stone
    HAMAMUKI Nao
    10th International Congress on Industrial and Applied Mathematics - ICIAM 2023, Aug. 2023, Invited oral presentation
    [Invited], [International presentation]
  • 非凸な石の摩耗過程における待ち時間効果
    HAMAMUKI Nao
    日本応用数理学会2022年度年会, Sep. 2022, Japanese, Invited oral presentation
    [Invited]
  • 平均曲率流方程式のゲーム解釈と動的境界値問題
    HAMAMUKI Nao
    日本数学会北海道支部講演会・支部総会, Dec. 2021, Japanese, Public discourse
    [Invited]
  • A lower spatially Lipschitz bound for solutions to fully nonlinear parabolic equations and its optimality
    HAMAMUKI Nao
    偏微分方程式セミナー（北海道大学）, Oct. 2021, Japanese, Public discourse
    [Invited]
  • A lower spatially Lipschitz bound for solutions to fully nonlinear parabolic equations and its optimality
    HAMAMUKI Nao
    広島微分方程式研究会, Oct. 2021, Japanese, Invited oral presentation
    [Invited]
  • Asymptotic behavior of viscosity solutions to the mean curvature flow equation with discontinuous source terms
    HAMAMUKI Nao
    RIMS共同研究（公開型）『偏微分方程式の解の幾何的様相』, Jun. 2021, Japanese, Invited oral presentation
    [Invited]
  • Asymptotic behavior of solutions to level-set mean curvature flow equations with discontinuous source terms
    HAMAMUKI Nao
    Interfacial Phenomena in Reaction-Diffusion Systems, Aug. 2020, English, Invited oral presentation
    [Invited]
  • Two-dimensional nucleation in crystal growth and large time behavior of solutions
    HAMAMUKI Nao
    The 37th Kyushu Symposium on Partial Differential Equations, Jan. 2020, English, Invited oral presentation
    [Invited]
  • On large time behavior of some crystal growth problems
    HAMAMUKI Nao
    Mathematical Aspects of Surface and Interface Dynamics 18, Oct. 2019, English, Invited oral presentation
    [Invited], [International presentation]
  • Asymptotic shape of solutions to the mean curvature flow equation with discontinuous source terms
    HAMAMUKI Nao
    9th International Congress on Industrial and Applied Mathematics - ICIAM 2019, Jul. 2019, English, Invited oral presentation
    [Invited], [International presentation]
  • A comparison principle for viscosity solutions of a boundary value problem without the normal derivative
    HAMAMUKI Nao
    京都大学NLPDEセミナー, Jun. 2019, Japanese, Public discourse
    [Invited], [Domestic Conference]
  • Asymptotic shape of solutions to the mean curvature flow equation with discontinuous source terms
    HAMAMUKI Nao
    名古屋微分方程式セミナー, Apr. 2019, Japanese, Public discourse
    [Invited], [Domestic Conference]
  • Asymptotic shape of solutions to the mean curvature flow equation with discontinuous source terms
    HAMAMUKI Nao
    微分方程式と逆問題をめぐって, Mar. 2019, Japanese, Invited oral presentation
    [Invited], [Domestic Conference]
  • 不連続外力項を持つ曲率流方程式の粘性解について
    HAMAMUKI Nao
    第一回はこだて数理解析研究集会, Nov. 2018, Japanese, Invited oral presentation
    [Invited], [Domestic Conference]
  • On a dynamic boundary value problem of the level-set mean curvature flow equation
    HAMAMUKI Nao
    Advanced Developments for Surface and Interface Dynamics - Analysis and Computation, Jun. 2018, English, Invited oral presentation
    [Invited], [International presentation]
  • On a dynamic boundary condition for singular degenerate parabolic equations in a half space
    HAMAMUKI Nao
    日本数学会2018年度年会, Mar. 2018, Japanese, Oral presentation
    [Domestic Conference]
  • A discrete game interpretation for a dynamic boundary value problem of the mean curvature flow equation
    HAMAMUKI Nao
    京都大学NLPDEセミナー, Jan. 2018, Japanese, Public discourse
    [Invited], [Domestic Conference]
  • On viscosity solutions in metric spaces
    HAMAMUKI Nao
    離散幾何構造セミナー（北海道大学）, Dec. 2017, Japanese, Public discourse
    [Invited], [Domestic Conference]
  • On a dynamic boundary condition for singular degenerate parabolic equations
    HAMAMUKI Nao
    解析セミナー（神戸大学）, Dec. 2017, Japanese, Public discourse
    [Invited], [Domestic Conference]
  • A discrete game interpretation for a dynamic boundary value problem of the mean curvature flow equation
    HAMAMUKI Nao
    偏微分方程式セミナー（北海道大学）, Dec. 2017, Japanese, Public discourse
    [Invited], [Domestic Conference]
  • 界面発展方程式の動的境界値問題について
    HAMAMUKI Nao
    応用数学に関する勉強会（応用数学セミナー）＠芝浦工大, Nov. 2017, Japanese, Public discourse
    [Invited], [Domestic Conference]
  • 均質化問題と粘性解理論
    HAMAMUKI Nao
    日本応用数理学会2017年度年会, Sep. 2017, Japanese, Invited oral presentation
    [Invited], [Domestic Conference]
  • On surface evolutions under some dynamic boundary conditions
    HAMAMUKI Nao
    Nonlinear PDE for Future Applications -Optimal Control and PDE-, Jul. 2017, English, Invited oral presentation
    [Invited], [International presentation]
  • A comparison principle for singular degenerate parabolic equations under some dynamic boundary conditions
    HAMAMUKI Nao
    5th Italian-Japanese Workshop on Geometric Properties for Parabolic and Elliptic PDE's, May 2017, English, Invited oral presentation
    [Invited], [International presentation]
  • 粘性解に対する均質化問題ー不連続方程式への拡張とその応用ー
    HAMAMUKI Nao
    非線形現象の数値シミュレーションと解析2017, Mar. 2017, Japanese, Invited oral presentation
    [Invited], [Domestic Conference]
  • 不連続な加法的固有値問題に対する粘性解とその応用
    HAMAMUKI Nao
    金沢解析セミナー, Mar. 2017, Japanese, Public discourse
    [Invited], [Domestic Conference]
  • Two approaches to an approximation of a distance function to moving interfaces
    HAMAMUKI Nao
    第18回北東数学解析研究会, Feb. 2017, English, Invited oral presentation
    [Invited], [International presentation]
  • Two approaches to an approximation of a distance function to moving interfaces
    HAMAMUKI Nao
    Emerging Developments in Interfaces and Free Boundaries, Jan. 2017, English, Invited oral presentation
    [Invited], [International presentation]
  • Harnack inequalities for supersolutions of fully nonlinear elliptic difference equations
    HAMAMUKI Nao
    Towards regularity, Sep. 2016, English, Invited oral presentation
    [Invited], [International presentation]
  • On cell problems for Hamilton-Jacobi equations with non-coercive Hamiltonians and its application to homogenization problems
    HAMAMUKI Nao
    The 11th AIMS Conference on Dynamical Systems, Differential Equations and Applications, Jul. 2016, English, Invited oral presentation
    [Invited], [International presentation]
  • A discrete isoperimetric inequality on lattices
    HAMAMUKI Nao
    Hamilton-Jacobi Equations:New trends and applications, May 2016, English, Invited oral presentation
    [Invited], [International presentation]
■ Syllabus
  • 大学院共通授業科目（一般科目）：自然科学・応用科学, 2024年, 修士課程, 大学院共通科目
  • 数理科学概説, 2024年, 修士課程, 理学院
  • 微分積分学Ⅰ, 2024年, 学士課程, 全学教育
■ Affiliated academic society
  • THE MATHEMATICAL SOCIETY OF JAPAN
■ Research Themes
  • 界面発展方程式と粘性解の形状解析
    Grant-in-Aid for Scientific Research (C)
    Apr. 2023 - Mar. 2027
    HAMAMUKI Nao
    Japan Society for the Promotion of Science, 23K03175
  • 特異構造を持つ界面発展方程式と境界値問題
    Grant-in-Aid for Early-Career Scientists
    Apr. 2019 - Mar. 2023
    HAMAMUKI Nao
    Japan Society for the Promotion of Science, Principal investigator, Competitive research funding
  • Analysis of boundary value problems for fully nonlinear partial differential equations and its applications
    Research Grants
    Apr. 2018 - Mar. 2019
    HAMAMUKI Nao
    Inamori Foundation, Principal investigator, Competitive research funding
  • 離散と連続をつなぐ粘性解理論の構築
    Grant-in-Aid for Young Scientists (B)
    Apr. 2016 - Mar. 2019
    HAMAMUKI Nao
    Japan Society for the Promotion of Science, Principal investigator, Competitive research funding
  • 界面ダイナミクスの数学解析に向けた粘性解理論の深化
    Grant for Basic Science Research Projects
    Nov. 2015 - Oct. 2016
    HAMAMUKI Nao
    The Sumitomo Foundation, Principal investigator, Competitive research funding
  • Viscosity solutions on metric spaces
    Grants-in-Aid for Scientific Research
    Apr. 2013 - Mar. 2016
    GIGA Yoshikazu; ASAI Tomoro; OHTSUKA Takeshi; GIGA Mi-Ho; KURODA Hirotoshi; NAKAYASU Atsushi; HAMAMUKI Nao
    We consider the Eikonal equation in a space such as network or fractal, where the gradient of function is not well-defined in canonical way. We establish the theory of viscosity solutions in a general metric space. We also establish the theory of viscosity solutions for a curvature flow equation describing motion of a surface of a crystal or a grain boundary, especially a crystalline curvature flow, which has a strong anisotropy, when the surface is regarded as a curve. A curvature flow with strong anisotropy is regarded at least formally as a gradient flow of area measured by non-Euclidean metric in a suitable metric space. However, a general theory is not yet established so we study the problem individually.
    Japan Society for the Promotion of Science, Grant-in-Aid for Challenging Exploratory Research, The University of Tokyo, 25610025
  • 粘性解理論とその材料科学分野への応用
    Grant-in-Aid for JSPS Research Fellow PD
    Apr. 2014 - Jan. 2015
    HAMAMUKI Nao
    Japan Society for the Promotion of Science, Principal investigator, Competitive research funding
  • 結晶成長現象とハミルトン・ヤコビ方程式
    Grant-in-Aid for JSPS Research Fellow DC1
    Apr. 2011 - Mar. 2014
    HAMAMUKI Nao
    平成25年度は、ハミルトン・ヤコビ方程式に対する等高而法の改良について研究した。等高面法は、結晶表面などに代表される曲面(界面)の運動を追跡するための技法で、各時刻における曲面をある補助関数のゼロ等高面として表示し, その補助関数に対する偏微分方程式(等高面方税式)を解くことで曲面の動きを求める。しかし時間が経つにつれて解の傾きが小さくなることがあり, このとき計算機では等高面を正確に取り出せなくなるという問題がある。そこで、元の等高面方程式を適当に修正することで、傾きが小さくならない解を得ることを目的に研究を行った。界面への符号付き距離関数は傾きが1であるという事実に着目し、1 : 符号付き距離関数との比較、2 : 符号付き距離関数への収束、という二つのアプローチに基づいて修正方程式を導入した。以下にその内容と成果を述べる。
    1 : 界面運動が滑らかであると仮定し、その界面への符号付き距離関数が満たす方程式をテイラー展開して得られる方程式を修正方程式として採用した。そして、初期値が初期界面付近で符号付き距離関数に等しいとき、初期値問題の粘性解が時間大域的にも符号付き距離関数に十分近いことを、比較定理を用いて証明した。
    2 : 元の等高面方程式に、解の傾きを1に補正する効果を持つ項を付け加えた方程式を修正方程式として採用した。そして、補正項の係数であるパラメータを無限大にしたときに、初期値問題の粘性解が界面への符号付き距離関数へと収束することを証明した。また、この修正力程式は、元の等高面方程式と、時間微分が補正項に等しいという方程式とを交互に解く操作を考えたときに、その時間幅を0にしたときの極限を考えることで得られることも明らかにした。これは、時間に関しての均質化理論の応用として示される。この二つの方程式を解く時間比が、修正方程式のパラメータとして現れることも分かった。
    Japan Society for the Promotion of Science, 特別研究員奨励費, 東京大学, Principal investigator, Competitive research funding, 11J04365