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Hamamuki Nao  浜向 直

ORCIDConnect your ORCID iD *help
Researcher Number 70749754
Other IDs
Affiliation (Current) 2025: 北海道大学, 理学研究院, 准教授
Affiliation (based on the past Project Information) *help 2016 – 2023: 北海道大学, 理学研究院, 准教授
Review Section/Research Field
Principal Investigator
Basic Section 12020:Mathematical analysis-related / Mathematical analysis
Keywords
Principal Investigator
比較定理 / 粘性解 / 界面発展方程式 / 完全非線形楕円型方程式 / 動的境界条件 / ハミルトン・ヤコビ方程式 / 平均曲率流方程式 / 決定論的ゲーム / 動的境界値問題 / 形状解析 … More / 最大値原理 / 完全非線形放物型方程式 / 勾配評価 / ガウス曲率流方程式 / 結晶成長 / 応用数学 / 解析学 / 関数方程式論 / 等高面法 Less
  • Research Projects

    (3 results)
  • Research Products

    (62 results)
  • Co-Researchers

    (3 People)
  •  Surface evolution equations and geometric analysis of viscosity solutionsPrincipal Investigator

    • Principal Investigator
      浜向 直
    • Project Period (FY)
      2023 – 2026
    • Research Category
      Grant-in-Aid for Scientific Research (C)
    • Review Section
      Basic Section 12020:Mathematical analysis-related
    • Research Institution
      Hokkaido University
  •  Surface evolution equations with singular structure and boundary value problemsPrincipal Investigator

    • Principal Investigator
      浜向 直
    • Project Period (FY)
      2019 – 2024
    • Research Category
      Grant-in-Aid for Early-Career Scientists
    • Review Section
      Basic Section 12020:Mathematical analysis-related
    • Research Institution
      Hokkaido University
  •  Construction of the viscosity solution theory connecting continuous problems and discrete problemsPrincipal Investigator

    • Principal Investigator
      Hamamuki Nao
    • Project Period (FY)
      2016 – 2019
    • Research Category
      Grant-in-Aid for Young Scientists (B)
    • Research Field
      Mathematical analysis
    • Research Institution
      Hokkaido University

All 2023 2022 2021 2020 2019 2018 2017 2016

All Journal Article Presentation

  • [Journal Article] Weak comparison principles for fully nonlinear degenerate parabolic equations with discontinuous source terms2023

    • Author(s)
      Nao Hamamuki, Kuniyasu Misu
    • Journal Title

      Minimax Theory and its Applications

      Volume: 8 Pages: 37-60

    • NAID

      120007181797

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-19K14564
  • [Journal Article] A dynamical approach to lower gradient estimates for viscosity solutions of Hamilton-Jacobi equations2023

    • Author(s)
      Nao Hamamuki, Kazuya Hirose
    • Journal Title

      SIAM Journal on Mathematical Analysis

      Volume: 55 Issue: 4 Pages: 3169-3204

    • DOI

      10.1137/22m1480483

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-19K14564, KAKENHI-PROJECT-23K03175
  • [Journal Article] A dynamical approach to lower gradient estimates for viscosity solutions of Hamilton-Jacobi equations2023

    • Author(s)
      Nao Hamamuki, Kazuya Hirose,
    • Journal Title

      SIAM Journal on Mathematical Analysis

      Volume: -

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-19K14564
  • [Journal Article] A lower spatially Lipschitz bound for solutions to fully nonlinear parabolic equations and its optimality2023

    • Author(s)
      Nao Hamamuki, Suguru Kikkawa
    • Journal Title

      Indiana University Mathematics Journal

      Volume: 72 Issue: 2 Pages: 455-487

    • DOI

      10.1512/iumj.2023.72.9333

    • NAID

      120006882102

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-19K14564, KAKENHI-PROJECT-23K03175
  • [Journal Article] A lower spatially Lipschitz bound for solutions to fully nonlinear parabolic equations and its optimality2022

    • Author(s)
      Nao Hamamuki, Suguru Kikkawa
    • Journal Title

      Indiana University Mathematics Journal

      Volume: -

    • NAID

      120006882102

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-19K14564
  • [Journal Article] A weak comparison principle and asymptotic behavior of viscosity solutions to the mean curvature flow equation with discontinuous source terms2022

    • Author(s)
      Nao Hamamuki, Kuniyasu Misu
    • Journal Title

      RIMS Kokyuroku

      Volume: 2212 Pages: 41-53

    • Open Access
    • Data Source
      KAKENHI-PROJECT-19K14564
  • [Journal Article] A self-affine property of evolutional type appearing in a Hamilton--Jacobi flow starting from the Takagi function2021

    • Author(s)
      Fujita, Y., Hamamuki,N., , Yamaguchi,N.
    • Journal Title

      to appear in Michigan Mathematical Journal

      Volume: 70 Issue: 1 Pages: 1-16

    • DOI

      10.1307/mmj/20195782

    • Peer Reviewed / Open Access / Int'l Joint Research
    • Data Source
      KAKENHI-PROJECT-18K03360, KAKENHI-PROJECT-19K14564, KAKENHI-PROJECT-21K03322
  • [Journal Article] A game-theoretic approach to dynamic boundary problems for level-set curvature flow equations and applications2021

    • Author(s)
      Nao Hamamuki, Qing Liu
    • Journal Title

      SN Partial Differential Equations and Applications

      Volume: 2 Issue: 2 Pages: 1-27

    • DOI

      10.1007/s42985-021-00076-w

    • Peer Reviewed / Open Access
    • Data Source
      KAKENHI-PROJECT-19K14564, KAKENHI-PROJECT-19K03574
  • [Journal Article] All the generalized characteristics for the solution to a Hamilton--Jacobi equation with the initial data of the Takagi function2020

    • Author(s)
      Fujita, Y., Hamamuki,N., , Yamaguchi,N.
    • Journal Title

      SN Partial Differential Equations and Applications "Viscosity solutions - Dedicated to Hitoshi Ishii on the award of the 1st Kodaira Kunihiko Prize"

      Volume: 1:38 Issue: 6 Pages: 1-20

    • DOI

      10.1007/s42985-020-00039-7

    • Peer Reviewed / Int'l Joint Research
    • Data Source
      KAKENHI-PROJECT-18K03360, KAKENHI-PROJECT-19K14564
  • [Journal Article] A self-affine property of evolutional type appearing in a Hamilton-Jacobi flow starting from the Takagi function2020

    • Author(s)
      Yasuhiro Fujita, Nao Hamamuki, Norikazu Yamaguchi
    • Journal Title

      Michigan Mathematical Journal

      Volume: -

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-16K17621
  • [Journal Article] A deterministic game interpretation for fully nonlinear parabolic equations with dynamic boundary conditions2020

    • Author(s)
      Nao Hamamuki, Qing Liu
    • Journal Title

      ESAIM Control Optim. Calc. Var.

      Volume: 26 Pages: 1-42

    • DOI

      10.1051/cocv/2019076

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-19K03574, KAKENHI-PROJECT-19K14564, KAKENHI-PROJECT-16K17621
  • [Journal Article] A class of nowhere differentiable functions satisfying some concavity-type estimate2020

    • Author(s)
      Yasuhiro Fujita, Nao Hamamuki, Antonio Siconolfi, Norikazu Yamaguchi
    • Journal Title

      Acta Mathematica Hungarica

      Volume: 160 Issue: 2 Pages: 343-359

    • DOI

      10.1007/s10474-019-01007-3

    • Peer Reviewed / Open Access / Int'l Joint Research
    • Data Source
      KAKENHI-PROJECT-19K14564, KAKENHI-PROJECT-16K17621, KAKENHI-PROJECT-18K03360
  • [Journal Article] An improvement of level set equations via approximation of a distance function2019

    • Author(s)
      Nao Hamamuki
    • Journal Title

      Applicable Analysis

      Volume: 98 Issue: 10 Pages: 1901-1915

    • DOI

      10.1080/00036811.2018.1484911

    • NAID

      120006382323

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-16K17621
  • [Journal Article] On a dynamic boundary condition for singular degenerate parabolic equations in a half space2018

    • Author(s)
      Yoshikazu Giga, Nao Hamamuki
    • Journal Title

      NoDEA. Nonlinear Differential Equations and Applications

      Volume: 25 Issue: 6

    • DOI

      10.1007/s00030-018-0542-6

    • NAID

      120006462293

    • Peer Reviewed
    • Data Source
      KAKENHI-PROJECT-16K17621, KAKENHI-PROJECT-16H03948
  • [Journal Article] A rigorous setting for the reinitialization of first order level set equations2016

    • Author(s)
      Nao Hamamuki, Eleftherios Ntovoris
    • Journal Title

      Interfaces and Free Boundaries

      Volume: 18 Issue: 4 Pages: 579-621

    • DOI

      10.4171/ifb/374

    • NAID

      120006459763

    • Peer Reviewed / Int'l Joint Research
    • Data Source
      KAKENHI-PROJECT-16K17621
  • [Presentation] Waiting time effects for the wearing process of a non-convex stone2023

    • Author(s)
      Nao Hamamuki
    • Organizer
      Geometric PDE and Applied Analysis Seminar
    • Invited / Int'l Joint Research
    • Data Source
      KAKENHI-PROJECT-19K14564
  • [Presentation] Waiting time effects for the wearing process of a non-convex stone2023

    • Author(s)
      Nao Hamamuki, Ryosuke Takahashi
    • Organizer
      10th International Congress on Industrial and Applied Mathematics - ICIAM 2023
    • Invited / Int'l Joint Research
    • Data Source
      KAKENHI-PROJECT-19K14564
  • [Presentation] A lower spatially Lipschitz bound for solutions to fully nonlinear parabolic equations and its optimality2023

    • Author(s)
      浜向直
    • Organizer
      鳥取PDE研究集会2023
    • Invited
    • Data Source
      KAKENHI-PROJECT-23K03175
  • [Presentation] Waiting time effects for the wearing process of a non-convex stone2023

    • Author(s)
      Nao Hamamuki
    • Organizer
      Geometric PDE and Applied Analysis Seminar
    • Invited / Int'l Joint Research
    • Data Source
      KAKENHI-PROJECT-23K03175
  • [Presentation] A lower spatially Lipschitz bound for solutions to fully nonlinear parabolic equations and its optimality2023

    • Author(s)
      浜向直
    • Organizer
      鳥取PDE研究集会2023
    • Invited
    • Data Source
      KAKENHI-PROJECT-19K14564
  • [Presentation] Waiting time effects for the wearing process of a non-convex stone2023

    • Author(s)
      Nao Hamamuki, Ryosuke Takahashi
    • Organizer
      10th International Congress on Industrial and Applied Mathematics - ICIAM 2023
    • Invited / Int'l Joint Research
    • Data Source
      KAKENHI-PROJECT-23K03175
  • [Presentation] A dynamical approach to lower gradient estimates for viscosity solutions of Hamilton-Jacobi equations2022

    • Author(s)
      浜向直, 廣瀬和也
    • Organizer
      日本数学会2022年度秋季総合分科会
    • Data Source
      KAKENHI-PROJECT-19K14564
  • [Presentation] 非凸な石の摩耗過程における待ち時間効果2022

    • Author(s)
      浜向直, 高橋怜甫
    • Organizer
      日本応用数理学会2022年度年会
    • Invited
    • Data Source
      KAKENHI-PROJECT-19K14564
  • [Presentation] Asymptotic shape of solutions to the mean curvature flow equation with discontinuous source terms2021

    • Author(s)
      浜向直, 三栖邦康
    • Organizer
      日本数学会2021年度秋季総合分科会
    • Data Source
      KAKENHI-PROJECT-19K14564
  • [Presentation] 平均曲率流方程式のゲーム解釈と動的境界値問題2021

    • Author(s)
      浜向直
    • Organizer
      日本数学会北海道支部講演会・支部総会
    • Invited
    • Data Source
      KAKENHI-PROJECT-19K14564
  • [Presentation] Asymptotic behavior of viscosity solutions to the mean curvature flow equation with discontinuous source terms2021

    • Author(s)
      浜向直
    • Organizer
      RIMS共同研究(公開型)『偏微分方程式の解の幾何的様相』
    • Invited
    • Data Source
      KAKENHI-PROJECT-19K14564
  • [Presentation] A lower spatially Lipschitz bound for solutions to fully nonlinear parabolic equations and its optimality2021

    • Author(s)
      浜向直
    • Organizer
      広島微分方程式研究会
    • Invited
    • Data Source
      KAKENHI-PROJECT-19K14564
  • [Presentation] A lower spatially Lipschitz bound for solutions to fully nonlinear parabolic equations and its optimality2021

    • Author(s)
      浜向直
    • Organizer
      偏微分方程式セミナー(北海道大学)
    • Invited
    • Data Source
      KAKENHI-PROJECT-19K14564
  • [Presentation] Two-dimensional nucleation in crystal growth and large time behavior of solutions2020

    • Author(s)
      Nao Hamamuki
    • Organizer
      第37回九州における偏微分方程式研究集会
    • Invited / Int'l Joint Research
    • Data Source
      KAKENHI-PROJECT-19K14564
  • [Presentation] 高木函数を初期値とするHamilton-Jacobi方程式における特異性の伝播2020

    • Author(s)
      藤田安啓, 浜向直, 山口範和
    • Organizer
      日本数学会2020年度秋季総合分科会
    • Data Source
      KAKENHI-PROJECT-19K14564
  • [Presentation] Two-dimensional nucleation in crystal growth and large time behavior of solutions2020

    • Author(s)
      Nao Hamamuki
    • Organizer
      第37回九州における偏微分方程式研究集会
    • Invited / Int'l Joint Research
    • Data Source
      KAKENHI-PROJECT-16K17621
  • [Presentation] Asymptotic behavior of solutions to level-set mean curvature flow equations with discontinuous source terms2020

    • Author(s)
      Nao Hamamuki
    • Organizer
      Interfacial Phenomena in Reaction-Diffusion Systems
    • Invited / Int'l Joint Research
    • Data Source
      KAKENHI-PROJECT-19K14564
  • [Presentation] A comparison principle for viscosity solutions of a boundary value problem without the normal derivative2019

    • Author(s)
      浜向 直
    • Organizer
      京都大学NLPDEセミナー
    • Invited
    • Data Source
      KAKENHI-PROJECT-19K14564
  • [Presentation] Asymptotic shape of solutions to the mean curvature flow equation with discontinuous source terms2019

    • Author(s)
      Nao Hamamuki
    • Organizer
      9th International Congress on Industrial and Applied Mathematics - ICIAM 2019
    • Int'l Joint Research
    • Data Source
      KAKENHI-PROJECT-19K14564
  • [Presentation] Asymptotic shape of solutions to the mean curvature flow equation with discontinuous source terms2019

    • Author(s)
      浜向 直
    • Organizer
      微分方程式と逆問題をめぐって
    • Invited
    • Data Source
      KAKENHI-PROJECT-16K17621
  • [Presentation] Asymptotic shape of solutions to the mean curvature flow equation with discontinuous source terms2019

    • Author(s)
      浜向 直
    • Organizer
      名古屋微分方程式セミナー
    • Invited
    • Data Source
      KAKENHI-PROJECT-19K14564
  • [Presentation] On large time behavior of some crystal growth problems2019

    • Author(s)
      Nao Hamamuki
    • Organizer
      表面・界面ダイナミクスの数理18
    • Invited / Int'l Joint Research
    • Data Source
      KAKENHI-PROJECT-19K14564
  • [Presentation] On large time behavior of some crystal growth problems2019

    • Author(s)
      Nao Hamamuki
    • Organizer
      表面・界面ダイナミクスの数理18
    • Invited / Int'l Joint Research
    • Data Source
      KAKENHI-PROJECT-16K17621
  • [Presentation] Asymptotic shape of solutions to the mean curvature flow equation with discontinuous source terms2019

    • Author(s)
      浜向 直
    • Organizer
      名古屋微分方程式セミナー
    • Invited
    • Data Source
      KAKENHI-PROJECT-16K17621
  • [Presentation] Hamilton-Jacobi方程式に現れる時間発展型のself-affine性2019

    • Author(s)
      藤田 安啓, 浜向 直, 山口 範和
    • Organizer
      日本数学会2019年度秋季総合分科会
    • Data Source
      KAKENHI-PROJECT-16K17621
  • [Presentation] A comparison principle for viscosity solutions of a boundary value problem without the normal derivative2019

    • Author(s)
      浜向 直
    • Organizer
      京都大学NLPDEセミナー
    • Invited
    • Data Source
      KAKENHI-PROJECT-16K17621
  • [Presentation] Asymptotic shape of solutions to the mean curvature flow equation with discontinuous source terms2019

    • Author(s)
      Nao Hamamuki
    • Organizer
      9th International Congress on Industrial and Applied Mathematics - ICIAM 2019
    • Invited / Int'l Joint Research
    • Data Source
      KAKENHI-PROJECT-16K17621
  • [Presentation] Hamilton-Jacobi方程式に現れる時間発展型のself-affine性2019

    • Author(s)
      藤田 安啓, 浜向 直, 山口 範和
    • Organizer
      日本数学会2019年度秋季総合分科会
    • Data Source
      KAKENHI-PROJECT-19K14564
  • [Presentation] 不連続外力項を持つ曲率流方程式の粘性解について2018

    • Author(s)
      浜向 直
    • Organizer
      第一回はこだて数理解析研究集会
    • Invited
    • Data Source
      KAKENHI-PROJECT-16K17621
  • [Presentation] A discrete game interpretation for a dynamic boundary value problem of the mean curvature flow equation2018

    • Author(s)
      浜向 直
    • Organizer
      京都大学NLPDEセミナー
    • Invited
    • Data Source
      KAKENHI-PROJECT-16K17621
  • [Presentation] On a dynamic boundary value problem of the level-set mean curvature flow equation2018

    • Author(s)
      Nao Hamamuki
    • Organizer
      Advanced Developments for Surface and Interface Dynamics - Analysis and Computation
    • Invited / Int'l Joint Research
    • Data Source
      KAKENHI-PROJECT-16K17621
  • [Presentation] On a dynamic boundary condition for singular degenerate parabolic equations in a half space2018

    • Author(s)
      浜向直, 儀我美一
    • Organizer
      日本数学会2018年度年会
    • Data Source
      KAKENHI-PROJECT-16K17621
  • [Presentation] 病的函数を初期値とするHamilton-Jacobi flowについて2018

    • Author(s)
      藤田安啓, 浜向直, Antonio Siconolfi, 山口範和
    • Organizer
      日本数学会2018年度年会
    • Data Source
      KAKENHI-PROJECT-16K17621
  • [Presentation] 界面発展方程式の動的境界値問題について2017

    • Author(s)
      浜向 直
    • Organizer
      応用数学に関する勉強会(応用数学セミナー)@芝浦工大
    • Invited
    • Data Source
      KAKENHI-PROJECT-16K17621
  • [Presentation] 均質化問題と粘性解理論2017

    • Author(s)
      浜向 直
    • Organizer
      日本応用数理学会2017年度年会
    • Invited
    • Data Source
      KAKENHI-PROJECT-16K17621
  • [Presentation] 不連続な加法的固有値問題に対する粘性解とその応用2017

    • Author(s)
      浜向 直
    • Organizer
      金沢解析セミナー
    • Place of Presentation
      金沢大学(石川県・金沢市)
    • Invited
    • Data Source
      KAKENHI-PROJECT-16K17621
  • [Presentation] Two approaches to an approximation of a distance function to moving interfaces2017

    • Author(s)
      Nao Hamamuki
    • Organizer
      第18回北東数学解析研究会
    • Place of Presentation
      東北大学(宮城県・仙台市)
    • Invited / Int'l Joint Research
    • Data Source
      KAKENHI-PROJECT-16K17621
  • [Presentation] On surface evolutions under some dynamic boundary conditions2017

    • Author(s)
      Nao Hamamuki
    • Organizer
      Nonlinear PDE for Future Applications -Optimal Control and PDE-
    • Invited / Int'l Joint Research
    • Data Source
      KAKENHI-PROJECT-16K17621
  • [Presentation] A comparison principle for singular degenerate parabolic equations under some dynamic boundary conditions2017

    • Author(s)
      Nao Hamamuki
    • Organizer
      5th Italian-Japanese Workshop on Geometric Properties for Parabolic and Elliptic PDE's
    • Invited / Int'l Joint Research
    • Data Source
      KAKENHI-PROJECT-16K17621
  • [Presentation] Two approaches to an approximation of a distance function to moving interfaces2017

    • Author(s)
      Nao Hamamuki
    • Organizer
      Emerging Developments in Interfaces and Free Boundaries
    • Place of Presentation
      オーベルヴォルファッハ(ドイツ)
    • Invited / Int'l Joint Research
    • Data Source
      KAKENHI-PROJECT-16K17621
  • [Presentation] On viscosity solutions in metric spaces2017

    • Author(s)
      浜向 直
    • Organizer
      離散幾何構造セミナー(北海道大学)
    • Invited
    • Data Source
      KAKENHI-PROJECT-16K17621
  • [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2017

    • Author(s)
      浜向 直
    • Organizer
      非線形現象の数値シミュレーションと解析2017
    • Place of Presentation
      北海道大学(北海道・札幌市)
    • Invited
    • Data Source
      KAKENHI-PROJECT-16K17621
  • [Presentation] A discrete game interpretation for a dynamic boundary value problem of the mean curvature flow equation2017

    • Author(s)
      浜向 直
    • Organizer
      偏微分方程式セミナー(北海道大学)
    • Invited
    • Data Source
      KAKENHI-PROJECT-16K17621
  • [Presentation] On a dynamic boundary condition for singular degenerate parabolic equations2017

    • Author(s)
      浜向 直
    • Organizer
      解析セミナー(神戸大学)
    • Invited
    • Data Source
      KAKENHI-PROJECT-16K17621
  • [Presentation] On cell problems for Hamilton-Jacobi equations with non-coercive Hamiltonians and its application to homogenization problems2016

    • Author(s)
      Nao Hamamuki
    • Organizer
      The 11th AIMS Conference on Dynamical Systems, Differential Equations and Applications
    • Place of Presentation
      オーランド(アメリカ合衆国)
    • Invited / Int'l Joint Research
    • Data Source
      KAKENHI-PROJECT-16K17621
  • [Presentation] A discrete isoperimetric inequality on lattices2016

    • Author(s)
      Nao Hamamuki
    • Organizer
      Hamilton-Jacobi Equations:New trends and applications
    • Place of Presentation
      レンヌ(フランス)
    • Invited / Int'l Joint Research
    • Data Source
      KAKENHI-PROJECT-16K17621
  • [Presentation] Harnack inequalities for supersolutions of fully nonlinear elliptic difference equations2016

    • Author(s)
      Nao Hamamuki
    • Organizer
      Towards regularity
    • Place of Presentation
      ワルシャワ(ポーランド)
    • Invited / Int'l Joint Research
    • Data Source
      KAKENHI-PROJECT-16K17621
  • 1.  YAMAGUCHI Norikazu
    # of Collaborated Projects: 0 results
    # of Collaborated Products: 2 results
  • 2.  藤田 安啓
    # of Collaborated Projects: 0 results
    # of Collaborated Products: 2 results
  • 3.  柳 青
    # of Collaborated Projects: 0 results
    # of Collaborated Products: 1 results

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