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Multifaceted analysis for stable structures of free-boundaries governed by nonlinear variational inequalities

Research Project

Project/Area Number 24740099
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeMulti-year Fund
Research Field Global analysis
Research InstitutionChiba University

Principal Investigator

Shirakawa Ken  千葉大学, 教育学部, 准教授 (50349809)

Project Period (FY) 2012-04-01 – 2016-03-31
Project Status Completed (Fiscal Year 2015)
Budget Amount *help
¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2015: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2014: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2013: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2012: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Keywords自由境界 / 非線形変分不等式 / 安定構造 / 多角的観点からの考察 / 力学系の観点 / 近似の観点 / 結晶粒界 / 統一的な解法 / 自由境界の構造解析 / 非等方的数学モデル / リアルな現象再現 / 仮似変分不等式 / 幾何学的滑らかさ / 緩和モデル / 力学的境界条件 / 結晶粒界の数学モデル / 放物型連立変分不等式 / 改良型モデル / Allen-Cahn 方程式 / 統一的な解析法 / 結晶構造の回転効果 / 定常解の構造 / 一般多次元モデル / 放物型変分不等式 / 特異拡散方程式 / 解の存在定理 / 時間離散化法 / 数値計算 / 薄膜磁性体 / 結晶粒界現象 / 幾何学的構造 / 安定性 / 変分不等式 / 劣微分作用素方程式
Outline of Final Research Achievements

The objective of the study is to observe the stable structures of free-boundaries from multifaceted viewpoints. The main advances are in the study of grain boundaries, and an original method which enables the uniform treatment of a number of mathematical models is established. In addition, some new research initiatives are obtained through the derivations of improved models which are coupled with heat exchanges, anisotropies, dynamic boundary conditions, and so on.

Report

(5 results)
  • 2015 Annual Research Report   Final Research Report ( PDF )
  • 2014 Research-status Report
  • 2013 Research-status Report
  • 2012 Research-status Report
  • Research Products

    (67 results)

All 2016 2015 2014 2013 2012 Other

All Int'l Joint Research (2 results) Journal Article (15 results) (of which Int'l Joint Research: 1 results,  Peer Reviewed: 10 results,  Open Access: 3 results,  Acknowledgement Compliant: 4 results) Presentation (42 results) (of which Int'l Joint Research: 5 results,  Invited: 4 results) Remarks (8 results)

  • [Int'l Joint Research] Universitat de Valencia(Spain)

    • Related Report
      2015 Annual Research Report
  • [Int'l Joint Research] Universita degli Studi di Pavia(Italy)

    • Related Report
      2015 Annual Research Report
  • [Journal Article] Large-time behavior for a PDE model of isothermal grain boundary motion with a constraint2015

    • Author(s)
      Ken Shirakawa, Hiroshi Watanabe
    • Journal Title

      Dynamical Systems and Differential Equations, AIMS Proceedings 2015, Proceedings of the 10th AIMS International Conference (Madrid, Spain)

      Volume: 1 Pages: 1009-1018

    • DOI

      10.3934/proc.2015.1009

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] Energy-dissipative solution to a one-dimensional phase field model of grain boundary motion2014

    • Author(s)
      K. Shirakawa and H. Watanabe
    • Journal Title

      Discrete Contin. Dyn. Syst. Ser. S

      Volume: 7 Issue: 1 Pages: 139-159

    • DOI

      10.3934/dcdss.2014.7.139

    • Related Report
      2014 Research-status Report
    • Peer Reviewed
  • [Journal Article] Existence of solutions to the Kobayashi-Warren-Carter system2014

    • Author(s)
      J. S. Moll and K. Shirakawa
    • Journal Title

      Calc. Var. Partial Differential Equations

      Volume: 51 Issue: 3-4 Pages: 621-656

    • DOI

      10.1007/s00526-013-0689-2

    • Related Report
      2014 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Stability for approximation methods of the onedimensional Kobayashi-Warren-Carter system2014

    • Author(s)
      H. Watanabe and K. Shirakawa
    • Journal Title

      Math. Bohem.

      Volume: 139 Pages: 381-389

    • Related Report
      2014 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] A one dimensional free boundary problem for adsorption phenomena2014

    • Author(s)
      N. Sato, T. Aiki, Y. Murase, K. Shirakawa
    • Journal Title

      Netw. Heterog. Media

      Volume: 9 Issue: 4 Pages: 655-668

    • DOI

      10.3934/nhm.2014.9.655

    • Related Report
      2014 Research-status Report
    • Peer Reviewed
  • [Journal Article] Existence for a PDE-model of a grain boundary motion involving solidification effect2014

    • Author(s)
      K. Shirakawa, H. Watanabe and N. Yamazaki
    • Journal Title

      New Role of the Theory of Abstract Evolution Equations -From a Point of View Overlooking the Individual Partial Differential Equations-, RIMS KoKyuroku

      Volume: 1856 Pages: 52-72

    • Related Report
      2014 Research-status Report
    • Open Access
  • [Journal Article] Parabolic systems consisting of Allen-Cahn type equations and Kobayashi-Warren-Carter models of grain boundary motions2014

    • Author(s)
      K. Shirakawa
    • Journal Title

      Proceedings of the conference: Functional Analysis and Applications, Evolution Equations and Control Theory, Kobe Univ.

      Volume: なし Pages: 151-162

    • Related Report
      2014 Research-status Report
    • Open Access / Acknowledgement Compliant
  • [Journal Article] Limiting observations for planar free-boundaries governed by isotropic-anisotropic singular diffusions2013

    • Author(s)
      K. Shirakawa
    • Journal Title

      Advances in Differential Equations

      Volume: 18 Pages: 351-382

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] Optimal control problems of phase field sysyem with total variation functional as the interfacial energy2013

    • Author(s)
      K. Shirakawa and N. Yamazaki
    • Journal Title

      Advances in Differential Equations

      Volume: 18 Pages: 309-350

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] Solvability for one-dimensional phase field system associated with grain boundary motion2013

    • Author(s)
      K. Shirakawa, H. Watanabe and N. Yamazaki
    • Journal Title

      Math. Ann

      Volume: 356 Issue: 1 Pages: 301-330

    • DOI

      10.1007/s00208-012-0849-2

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] Qualitative properties of a one-dimensional phase-field system associated with grain boundary2013

    • Author(s)
      H. Watanabe and K. Shirakawa
    • Journal Title

      GAKUTO Internat. Ser. Math. Sci. Appl.

      Volume: 36 Pages: 301-328

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] Phase field systems of grain boundaries with solidification effects2013

    • Author(s)
      K. Shirakawa
    • Journal Title

      Proceedings of the 38th Sapporo Symposium on Partial Differential Equations, Hokkaido University Technical Report Series in Mathematics

      Volume: 159 Pages: 44-53

    • Related Report
      2013 Research-status Report
  • [Journal Article] A mathematical model for a hysteresis appearing in adsorption phenomena2013

    • Author(s)
      T. Aiki, Y. Murase, N. Sato and K. Shirakawa
    • Journal Title

      New developments of the theory of evolution equations in the analysis of non-equilibria, RIMS Kokyuroku

      Volume: 1856 Pages: 1-11

    • Related Report
      2013 Research-status Report
  • [Journal Article] Time-discretization approach to various parabolic systems associated with grain boundaries2013

    • Author(s)
      K. Shirakawa
    • Journal Title

      Proceedings of Seminar on Partial Differential Equations in Osaka 2012 : in honor of Professor Hiroki Tanabe’s 80th birthday (http://hdl.handle.net/11094/24563)

      Volume: 無 Pages: 173-182

    • Related Report
      2012 Research-status Report
  • [Journal Article] Variational inequalities for a system of elliptic-parabolic equations2012

    • Author(s)
      M.Kubo
    • Journal Title

      J. Math. Anal. Appl.

      Volume: Volume 387, Issue 2 Issue: 2 Pages: 490-511

    • DOI

      10.1016/j.jmaa.2011.09.008

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Presentation] 異方性を加味した結晶粒界運動のフェーズ・フィールドモデルに対する エネルギー消散性.2016

    • Author(s)
      白川 健; 渡邉 紘; Moll, S.:
    • Organizer
      2016 日本数学会年会(実函数論)
    • Place of Presentation
      筑波大学(茨城)
    • Year and Date
      2016-03-16
    • Related Report
      2015 Annual Research Report
  • [Presentation] 異方性の効果を取り入れた結晶粒界モデルの可解性.2015

    • Author(s)
      白川 健; 渡邉 紘; Moll, S.:
    • Organizer
      第41 回発展方程式研究会
    • Place of Presentation
      日本女子大学目白キャンパス(東京)
    • Year and Date
      2015-12-25
    • Related Report
      2015 Annual Research Report
  • [Presentation] 結晶粒界の非等温系モデルのエネルギー消散解と漸近挙動.2015

    • Author(s)
      渡邉 紘; 白川 健; 山崎 教昭:
    • Organizer
      第41 回発展方程式研究会
    • Place of Presentation
      日本女子大学目白キャンパス(東京)
    • Year and Date
      2015-12-25
    • Related Report
      2015 Annual Research Report
  • [Presentation] Mathematical analysis for Kobayashi-Warren-Carter type models of grain boundary motions.2015

    • Author(s)
      Shirakawa, K.; Watanabe, H.; Moll, S.:
    • Organizer
      Mathematical Aspects of Surface and Interface Dynamics X
    • Place of Presentation
      Univ. Tokyo, Tokyo (Japan)
    • Year and Date
      2015-10-28
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Anisotropic models for grain boundary motions of Kobayashi-Warren-Carter types.2015

    • Author(s)
      Shirakawa, K.; Watanabe, H.; Moll, S.:
    • Organizer
      Devlopments of the theory of evolution equations as the applications to the analysis for nonlinear phenomena
    • Place of Presentation
      RIMS, Kyoto Univ., Kyoto (Japan)
    • Year and Date
      2015-10-21
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research
  • [Presentation] 異方性を加味した結晶粒界運動のKobayashi-Warren-Carter 型数学モ デル.2015

    • Author(s)
      白川 健; 渡邉 紘; Moll, S.:
    • Organizer
      2015 日本数学会秋季総合分科会(実函数論)
    • Place of Presentation
      京都産業大学(京都)
    • Year and Date
      2015-09-15
    • Related Report
      2015 Annual Research Report
  • [Presentation] 結晶粒界現象を記述する非等温系数学モデルに対する解の漸近挙動.2015

    • Author(s)
      渡邉 紘; 白川 健; 山崎 教昭:
    • Organizer
      2015 日本数学会秋季総合分科会(実函数論)
    • Place of Presentation
      京都産業大学(京都)
    • Year and Date
      2015-09-15
    • Related Report
      2015 Annual Research Report
  • [Presentation] Coupling systems of Fix-Caginalp type models and Kobayashi-Warren- Carter type models.2015

    • Author(s)
      白川 健; 渡邉 紘; 山崎 教昭:
    • Organizer
      2015 秋の偏微分方程式セミナー
    • Place of Presentation
      大阪大学待兼山会館(大阪)
    • Year and Date
      2015-09-10
    • Related Report
      2015 Annual Research Report
  • [Presentation] Energy-dissipations in non-isothermal phase-field systems associated with grain boundary motions.2015

    • Author(s)
      Shirakawa, K.; Watanabe, H.; Yamazaki, N.:
    • Organizer
      Mathematics for Nonlinear Phenomena: Analysis and Computation (MNP 2015)
    • Place of Presentation
      Sapporo Convention Center, Sapporo (Japan)
    • Year and Date
      2015-08-16
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Kobayashi-Warren-Carter type models of grain boundary motions with anisotropies.2015

    • Author(s)
      Shirakawa, K.; Watanabe, H.; Moll, S.:
    • Organizer
      The 8th International Congress on Industrial and Applied Mathematics (ICIAM 2015)
    • Place of Presentation
      China National Convention Center, Beijing (China)
    • Year and Date
      2015-08-10
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Energy dissipations for non-isothermal models of grain boundary motions.2015

    • Author(s)
      Shirakawa, K.; Watanabe, H.; Yamazaki, N.:
    • Organizer
      Equadiff 2015
    • Place of Presentation
      Universite Claude Bernard Lyon 1, Lyon (France)
    • Year and Date
      2015-07-06
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research
  • [Presentation] 非等温条件下における結晶粒界現象のフェーズ・フィールドモデル2015

    • Author(s)
      白川 健, 渡邉 紘
    • Organizer
      2015 日本数学会年会(実函数論)
    • Place of Presentation
      明治大学(東京)
    • Year and Date
      2015-03-21 – 2015-03-24
    • Related Report
      2014 Research-status Report
  • [Presentation] 結晶粒界の異方性を考慮した数学モデル2015

    • Author(s)
      白川 健, 渡邉 紘, J. S. Moll
    • Organizer
      第5 回非線形数理科学
    • Place of Presentation
      ながおか市民センター2F 2B 会議室(新潟)
    • Year and Date
      2015-02-21 – 2015-02-22
    • Related Report
      2014 Research-status Report
  • [Presentation] 結晶粒界現象の非等温系モデルの可解性2014

    • Author(s)
      白川 健, 渡邉 紘, 山崎 教昭
    • Organizer
      第40 回発展方程式研究会
    • Place of Presentation
      日本女子大学目白キャンパス(東京)
    • Year and Date
      2014-12-25 – 2014-12-27
    • Related Report
      2014 Research-status Report
  • [Presentation] Nonisothermal phase field systems of grain boundary motions2014

    • Author(s)
      J. S. Moll, K. Shirakawa, H. Watanabe and N. Yamazaki
    • Organizer
      Seminario de Analisis Matematico, Universitat de Valencia
    • Place of Presentation
      Departamento de Analisis Matematico Universitat de Valencia (Spain)
    • Year and Date
      2014-12-02
    • Related Report
      2014 Research-status Report
  • [Presentation] Kobayashi-Warren-Carter type systems of grain boundary motion2014

    • Author(s)
      K. Shirakawa, J. S. Moll and H. Watanabe
    • Organizer
      Special Meeting with Professor Augusto Visintin
    • Place of Presentation
      Conference room, Building 11, 4F, Bukkyo Univ. (Kyoto)
    • Year and Date
      2014-10-24 – 2014-10-25
    • Related Report
      2014 Research-status Report
  • [Presentation] 凝固現象と結晶粒界現象の等温系カップリングモデルにおけるエネルギー 消散解2014

    • Author(s)
      白川 健, 渡邉 紘
    • Organizer
      2014 日本数学会年度秋季総合分科会(実函数論)
    • Place of Presentation
      広島大学(広島)
    • Year and Date
      2014-09-25 – 2014-09-28
    • Related Report
      2014 Research-status Report
  • [Presentation] Allen-Cahn 方程式と結晶粒界モデルによる連立系の時刻無限大における 解挙動2014

    • Author(s)
      渡邉 紘, 白川 健
    • Organizer
      2014 日本数学会年度秋季総合分科会(実函数論)
    • Place of Presentation
      広島大学(広島)
    • Year and Date
      2014-09-25 – 2014-09-28
    • Related Report
      2014 Research-status Report
  • [Presentation] Energy dissipations for mathematical models of grain boundary motions with isothermal solidifications2014

    • Author(s)
      K. Shirakawa, J. S. Moll and H. Watanabe
    • Organizer
      The 10th AIMS Conference on Dynamical Systems, Differential Equations and Applications
    • Place of Presentation
      Instituto de Ciencias Matematicas, Universidad Autonoma de Madrid, Madrid (Spain)
    • Year and Date
      2014-07-07 – 2014-07-11
    • Related Report
      2014 Research-status Report
  • [Presentation] 凝固による界面拡散を考慮した結晶粒界モデルにおけるエネルギー消散性2014

    • Author(s)
      白川 健
    • Organizer
      第123 回神楽坂解析セミナー
    • Place of Presentation
      東京理科大学神楽坂校舎(東京)
    • Year and Date
      2014-05-24
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] 結晶粒界現象に対する凝固による界面拡散を考慮した数学モデル2014

    • Author(s)
      白川 健, 渡邉 紘, 山崎 教昭
    • Organizer
      2014 日本数学会年会 (実函数論)
    • Place of Presentation
      学習院大学 (東京)
    • Related Report
      2013 Research-status Report
  • [Presentation] A phase field system of grain boundary generated by unknown-dependent total variation2013

    • Author(s)
      K. Shirakawa and S. Moll
    • Organizer
      Nonlinear Partial Differential Equations - On the occasion of J. M. Mazon's 60th birthday -
    • Place of Presentation
      University of Valencia, Valencia (Spain)
    • Related Report
      2013 Research-status Report
  • [Presentation] Phase field systems of grain boundaries with solidification effects2013

    • Author(s)
      K. Shirakawa, S. Moll and H. Watanabe
    • Organizer
      The 38th Sapporo Symposium on Partial Differential Equations
    • Place of Presentation
      Hokkaido University, Sapporo (Japan)
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] Energy-dissipations in multidimensional Kobayashi-Warren-Carter models of grain boundaries2013

    • Author(s)
      H. Watanabe, K. Shirakawa and S. Moll
    • Organizer
      Equadiff 13
    • Place of Presentation
      Charles University in Prague, Prague (Czech Republic)
    • Related Report
      2013 Research-status Report
  • [Presentation] Coupling models of phase transitions and grain boundary motions2013

    • Author(s)
      K. Shirakawa, H. Watanabe and S. Moll
    • Organizer
      Workshop "DIMO-2013" Diffuse Interface Models
    • Place of Presentation
      Hotel Bellavista, Levico (Italy)
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] 結晶粒界の放物型フェーズ・フィールドモデルにおける平滑化効果とエネルギー消散性2013

    • Author(s)
      白川 健, 渡邉 紘
    • Organizer
      2013 日本数学会秋季総合分科会 (実函数論)
    • Place of Presentation
      愛媛大学城北キャンパス (愛媛)
    • Related Report
      2013 Research-status Report
  • [Presentation] 結晶粒界現象を記述する退化性を伴う1次元数学モデルに対する定性的性質2013

    • Author(s)
      渡邉 紘, 白川 健
    • Organizer
      2013 日本数学会秋季総合分科会 (実函数論)
    • Place of Presentation
      愛媛大学城北キャンパス (愛媛)
    • Related Report
      2013 Research-status Report
  • [Presentation] Control problems of phase field systems associated with total variation energy2013

    • Author(s)
      山崎 教昭, 白川 健
    • Organizer
      2013 日本数学会秋季総合分科会 (実函数論)
    • Place of Presentation
      愛媛大学城北キャンパス (愛媛)
    • Related Report
      2013 Research-status Report
  • [Presentation] Gradient systems associated with grain boundary motions2013

    • Author(s)
      K. Shirakawa, H. Watanabe, N. Yamazaki and S. Moll
    • Organizer
      Workshop on Free Boundaries in Laplacian Growth Phenomena and Related Topics
    • Place of Presentation
      Kawai Hall, Tohoku University, Sendai (Japan)
    • Related Report
      2013 Research-status Report
  • [Presentation] On Warren-Kobayashi-Lobkovski-Carter type models of grain boundary motions2013

    • Author(s)
      K. Shirakawa, H. Watanabe, N. Yamazaki and S. Moll
    • Organizer
      New Role of the Theory of Abstract Evolution Equation - From a Point of View Overlooking the Individual Partial Differential Equations -
    • Place of Presentation
      RIMS, Kyoto University, Kyoto (Japan)
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] Allen-Cahn 型方程式と結晶粒界モデルによる連立偏微分方程式2013

    • Author(s)
      白川 健, 渡邉 紘, 山崎 教昭, モール サルヴァドール
    • Organizer
      第39回発展方程式研究会
    • Place of Presentation
      日本女子大学目白キャンパス (東京)
    • Related Report
      2013 Research-status Report
  • [Presentation] 退化性を伴う1次元Kobayashi-Warren-Carterモデルに対する定性的性質2013

    • Author(s)
      渡邉 紘, 白川 健
    • Organizer
      第39回発展方程式研究会
    • Place of Presentation
      日本女子大学目白キャンパス (東京)
    • Related Report
      2013 Research-status Report
  • [Presentation] 未知変数依存する測度と未知変数依存する特異拡散を含む放物型連立偏微分方程式2013

    • Author(s)
      白川 健, モール サルヴァドール
    • Organizer
      東工大数理解析研究会
    • Place of Presentation
      東京工業大学大岡山キャンパス (東京)
    • Related Report
      2012 Research-status Report
  • [Presentation] A nonstandard parabolic system associated with grain boundary motion2013

    • Author(s)
      K. Shirakawa, S. Moll
    • Organizer
      Functional Analysis and Applications - Evolution Equations and Control Theory -
    • Place of Presentation
      Takikawa Memorial Hall, Kobe Univ., Kobe (Japan)
    • Related Report
      2012 Research-status Report
  • [Presentation] 結晶粒界の一般多次元フェーズ・フィールドモデルに対する解の存在定理2013

    • Author(s)
      白川 健, モール サルヴァドール
    • Organizer
      2013 日本数学会年会 (実函数論分科会)
    • Place of Presentation
      京都大学吉田キャンパス (京都)
    • Related Report
      2012 Research-status Report
  • [Presentation] 吸着現象を表すある1次元自由境界問題の時間大域解の存在について2013

    • Author(s)
      佐藤 直紀, 愛木 豊彦, 村瀬 勇介, 白川 健
    • Organizer
      2013 日本数学会年会 (実函数論分科会)
    • Place of Presentation
      京都大学吉田キャンパス (京都)
    • Related Report
      2012 Research-status Report
  • [Presentation] 結晶粒界のフェーズ・フィールドモデルに対する数理解析2013

    • Author(s)
      白川 健, モール サルヴァドール
    • Organizer
      逆問題とその周辺分野に関するミニワークショップ
    • Place of Presentation
      東京大学数理科学研究科 (東京)
    • Related Report
      2012 Research-status Report
  • [Presentation] A phase field system motivated by grain boundary motion with degeneracy2012

    • Author(s)
      K. Shirakawa and H. Watanabe
    • Organizer
      12th International Conference on Free Boundary Problems: Theory and Applications
    • Place of Presentation
      Frauenchiemsee (Germany)
    • Related Report
      2012 Research-status Report
  • [Presentation] Solvability for Kobayashi-Warren-Carter models of grain boundaries in general multidimensional spaces2012

    • Author(s)
      K. Shirakawa and S. Moll
    • Organizer
      5th Polish-Japanese Days on Nonlinear Analysis in Interdisciplinary Sciences
    • Place of Presentation
      Kansai Seminar House, Kyoto (Japan)
    • Related Report
      2012 Research-status Report
  • [Presentation] Solvability for a free boundary problem on adsorption2012

    • Author(s)
      N. Sato, T. Aiki, Y. Murase and K. Shirakawa
    • Organizer
      5th Polish-Japanese Days on Nonlinear Analysis in Interdisciplinary Sciences
    • Place of Presentation
      Kansai Seminar House, Kyoto (Japan)
    • Related Report
      2012 Research-status Report
  • [Presentation] 結晶粒界の Kobayashi-Warren-Carter モデルの一般多次元における解の存在2012

    • Author(s)
      白川 健, モール サルヴァドール
    • Organizer
      第38回発展方程式研究会
    • Place of Presentation
      日本女子大学目白キャンパス (東京)
    • Related Report
      2012 Research-status Report
  • [Presentation] 吸着現象を表すある1次元境界問題の解の存在について2012

    • Author(s)
      佐藤 直紀, 愛木 豊彦, 村瀬 勇介, 白川 健
    • Organizer
      第38回発展方程式研究会
    • Place of Presentation
      日本女子大学目白キャンパス (東京)
    • Related Report
      2012 Research-status Report
  • [Remarks] 研究者個人のwebページ

    • URL

      http://kenboich.jp/

    • Related Report
      2015 Annual Research Report
  • [Remarks] 教育学部研究活動報告

    • URL

      http://www.education.chiba-u.jp/approach/facultyact/

    • Related Report
      2015 Annual Research Report
  • [Remarks] 千葉大学教育学部教員一覧DB

    • URL

      http://www.education.chiba-u.jp/home/staffTop/staff_011/

    • Related Report
      2015 Annual Research Report
  • [Remarks] 千葉大学教育学部研究活動報告

    • URL

      http://www.education.chiba-u.jp/approach/facultyact/

    • Related Report
      2014 Research-status Report
  • [Remarks] 研究者個人のページ

    • URL

      http://kenboich.jp/

    • Related Report
      2014 Research-status Report
  • [Remarks] 研究者個人webページ

    • URL

      http://www.kenboich.miraiserver.com/

    • Related Report
      2013 Research-status Report
  • [Remarks] 教育学部教員研究活動報告

    • URL

      http://www.edu.chiba-u.jp/approach/facultyact.html

    • Related Report
      2013 Research-status Report
  • [Remarks] 教育学部教員研究活動報告

    • URL

      http://www.edu.chiba-u.jp/approach/facultyact.html

    • Related Report
      2012 Research-status Report

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Published: 2013-05-31   Modified: 2019-07-29  

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