Nonlinear evolution equations with constraint related to the free boundary problem on thermohydraulics model

• Project/Area Number: 21740130
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Single-year Grants
• Research Field: Global analysis
• Research Institution: Kyoto University of Education
• Principal Investigator: FUKAO Takeshi 京都教育大学, 教育学部, 准教授 (00390469)
• Project Period (FY): 2008 – 2012
• Project Status: Completed (Fiscal Year 2012)
• Budget Amount: ¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000); Fiscal Year 2012: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2011: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2010: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000); Fiscal Year 2009: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
• Keywords: 発展方程式 / 熱水力学 / Navier-Stokes方程式 / 仮似変分不等式 / 制約問題 / Lagrange乗数 / 時間依存制約 / 非線形発展方程式 / 障害物問題 / ナヴィエ・ストークス方程式

Research Abstract

The solvability and the characterization of a solution for non linear evolution equations with constraint are treated. The problem is related to the free boundary problem on thermohydraulics model. The solvability for a system between the variational inequality of Navier-Stokes type and the heat equation is proved.

Research Products

• [Journal Article] Abstract theory of variational inequalities and Lagrange multipliers (2013)
  • Author(s): T. Fukao and N. Kenmochi
  • Journal Title: Discrete Contin. Dyn. Syst
  • Peer Reviewed
• [Journal Article] A thermohydraulics model with temperature dependent constraint on velocity fields (2013)
  • Author(s): Takeshi Fukao, Nobuyuki Kenmochi
  • Journal Title: Discrete Contin. Dyn. Syst. Ser. S Volume: 7
  • Peer Reviewed
• [Journal Article] Weak variational formulation for the constrained Navier-Stokes equations (2012)
  • Author(s): T. Fukao and N. Kenmochi
  • Journal Title: 京都大学数理解析研究所講究録 Volume: Vol. 1792 Pages: 57-81
• [Journal Article] Weak variational formulation for the constrained Navier-Stokes equations (2012)
  • Author(s): Takeshi Fukao, Nobuyuki Kenmochi
  • Journal Title: 京都大学数理解析研究所講究録 Volume: 1792 Pages: 57-81
• [Journal Article] Variational inequality of the Navier-Stokes equations with time-dependent constraint (2011)
  • Author(s): T. Fukao and N. Kenmochi
  • Journal Title: GAKUTO Internat. Ser. Math. Appl Volume: Vol. 34 Pages: 87-102
  • Peer Reviewed
• [Journal Article] Variational inequality for the Stokes equations with constraint (2011)
  • Author(s): T. Fukao
  • Journal Title: Discrete Contin.Dyn. Syst Pages: 437-446
  • Peer Reviewed
• [Journal Article] Variational inequality for the Navier-Stokes equations with time-dependent constraint (2011)
  • Author(s): T.Fukao, N.Kenmochi
  • Journal Title: GAKUTO International Series, Matematical Sciences and Applications Volume: Vol.34 Pages: 273-287
  • Peer Reviewed
• [Journal Article] Variational inequality for the Stokes equations with constraint (2011)
  • Author(s): T.Fukao
  • Journal Title: Discrete and continuous dynamical systems, supp Volume: supplement2011 Pages: 437-446
  • Peer Reviewed
• [Journal Article] Global attractor of double obstacle problem in thermohydraulics (2010)
  • Author(s): T. Fukao and M. Kubo
  • Journal Title: GAKUTO Internat. Ser. Math. Appl Volume: Vol. 32 Pages: 273-287
  • Peer Reviewed
• [Journal Article] Global attractor of double obstacle problem in thermohydraulics (2010)
  • Author(s): Takeshi Fukao, Masahiro Kubo
  • Journal Title: GAKUTO International Series, Matematical Sciences and Applications Volume: 32 Pages: 273-287
  • Peer Reviewed
• [Journal Article] Time-dependent obstacle problem in thermohydraulics (2009)
  • Author(s): T. Fukao and M. Kubo
  • Journal Title: Discrete Contin.Dyn. Syst Pages: 240-249
  • Peer Reviewed
• [Journal Article] Time-dependent obstacle problem in thermohydraulics (2009)
  • Author(s): Takeshi Fukao
  • Journal Title: Discrete and continuous dynamical systems, supplement supplement 2009 Pages: 240-249
  • Peer Reviewed
• [Journal Article] A thermohydraulics model with temperature dependent constraint on velocity fields
  • Author(s): T. Fukao and N. Kenmochi
  • Journal Title: Discrete Contin. Dyn. Syst. Ser S
  • Peer Reviewed
• [Presentation] Characterization of the solution for evolution equations with timed-ependent constraints (2013)
  • Author(s): 深尾武史-剣持信幸
  • Organizer: 日本数学会2013年度年会
  • Place of Presentation: 京都大学
• [Presentation] Characterization of the solution for evolution equations with time-dependent constraints (2013)
  • Author(s): 深尾 武史, 剣持 信幸
  • Organizer: 日本数学会2013年度年会
  • Place of Presentation: 京都大学
• [Presentation] ある種の非Newton流体を記述する変分不等式の可解性について (2012)
  • Author(s): 深尾武史
  • Organizer: 日本数学会2012年度年会実関数論分科会
  • Place of Presentation: 東京理科大学
  • Year and Date: 2012-03-28
• [Presentation] ある時間依存制約条件を含む発展方程式の解の表現定理について (2012)
  • Author(s): 深尾武史-剣持信幸
  • Organizer: 第38回発展方程式研究会
  • Place of Presentation: 日本女子大学
• [Presentation] On a variational inequality of Bingham and Navier-Stokes type in three dimensional space (2012)
  • Author(s): T. Fukao
  • Organizer: 5th Polish-Japanese Days on Nonline ar Mathematics inInterdisciplinary Sciences - Modellings, Analysis and Simulations -
  • Place of Presentation: 関西セミナーハウス, 京都
• [Presentation] On a variational inequality of Bingham and Navier-Stokes type in three dimension (2012)
  • Author(s): T. Fukao
  • Organizer: PDEs for multiphase advanced materials
  • Place of Presentation: Cortona, Italy
• [Presentation] Abstract theory of the variational inequality and Lagrange multiplier (2012)
  • Author(s): T. Fukao and N. Kenmochi
  • Organizer: AIMS' 9th International Conference on Dynamical Systems, Differentia Equations and Applicationsl
  • Place of Presentation: Orland, USA
• [Presentation] ある種の非Newton流体を記述する変分不等式の可解性について (2012)
  • Author(s): 深尾武史
  • Organizer: 日本数学会2012年度年会
  • Place of Presentation: 東京理科大学
• [Presentation] On a variational inequality for a fluid dynamics of Bingham and Navier-Stokes type in three dimension (2012)
  • Author(s): T. Fukao
  • Organizer: CONFERENCE ON Evolution Equations, Related Topics and Applications
  • Place of Presentation: 早稲田大学
• [Presentation] Abstract theory of the variational inequality and Lagrange multiplier (2012)
  • Author(s): Takeshi Fukao, Nobuyuki Kenmochi
  • Organizer: The 9th AIMS Conference on Dynamical Systems, Differential Equations and Applications
  • Place of Presentation: Orland, USA
• [Presentation] On a variational inequality of Bingham and Navier-Stokes type in three dimensional space (2012)
  • Author(s): Takeshi Fukao
  • Organizer: 5th Polish-Japanese Days on Nonlinear Mathematics in Interdisciplinary Sciences - Modellings, Analysis and Simulations -
  • Place of Presentation: 関西セミナーハウス, 京都
• [Presentation] Well-posedness for the variational inequality related to the Navier-Stokes equations (2011)
  • Author(s): Takeshi Fukao, Nobuyuki Kenmochi
  • Organizer: Analysis of non-equilibrium evolution problems : Selected topics in material and life sciences
  • Place of Presentation: オランダアイントフォーヘン工科大学
  • Year and Date: 2011-11-09
• [Presentation] Weak variational formulation for the Navier-Stokes equations with time-dependent constraint (2011)
  • Author(s): 深尾武史・剣持信幸
  • Organizer: 非平衡非線形現象の解析-発展方程式の立場から-
  • Place of Presentation: 京都大学
  • Year and Date: 2011-10-25
• [Presentation] 流速の大きさの制約条件に対する変分不等式の可解性について (2011)
  • Author(s): Takeshi Fukao, Nobuyuki Kenmochi
  • Organizer: 日本数学会2011年度秋季総合分科会実関数論分科会
  • Place of Presentation: 信州大学
  • Year and Date: 2011-09-29
• [Presentation] 流れの制約条件に対する変分不等式 (2011)
  • Author(s): 深尾武史
  • Organizer: International Symposium on Computational Science 2011
  • Place of Presentation: 金沢大学
  • Year and Date: 2011-02-16
• [Presentation] 流速の制約条件を含む強変分・弱変分形式とその可解性について (2011)
  • Author(s): 深尾武史-剣持信幸
  • Organizer: 第37回発展方程式研究会
  • Place of Presentation: 岐阜大学
• [Presentation] Well-posedness for the variational inequality related to the Navier-Stokes equations wth time-dependent constraints (2011)
  • Author(s): T. Fukao and N. Kenmochi
  • Organizer: Analysis of nonlinear evolution problems: Selected topics in material and life sciences
  • Place of Presentation: TU Eindhoven, Netherlands
• [Presentation] Weak variational formulation for the Navier-Stokes equations with time-dependent constraint (2011)
  • Author(s): T. Fukao and N. Kenmochi
  • Place of Presentation: 京都大学数理解析研究所
• [Presentation] 流速の大きさの制約条件に対する変分不等式の可解性について (2011)
  • Author(s): 深尾武史-剣持信幸
  • Organizer: 日本数学会2011年度秋季総合分科会
  • Place of Presentation: 信州大学
• [Presentation] Variational inequality for the Navier-Stokes equations with time dependent constraint (2011)
  • Author(s): T. Fukao and N. Kenmochi
  • Organizer: International Symposium on Computational Science 2011
  • Place of Presentation: 金沢大学
• [Presentation] 指示関数の劣微分による制約を含む流れの方程式の可解性について (2010)
  • Author(s): 深尾武史
  • Organizer: 第36回発展方程式研究会
  • Place of Presentation: 中央大学
  • Year and Date: 2010-12-24
• [Presentation] 流れの制約条件に対する変分不等式 (2010)
  • Author(s): 深尾武史
  • Organizer: 日本数学会 秋季総合分科会
  • Place of Presentation: 名古屋大学
  • Year and Date: 2010-09-25
• [Presentation] 指示関数の劣微分による制約を含む流れの方程式の可解性について (2010)
  • Author(s): 深尾武史
  • Organizer: 第2回 若手による流体セミナー
  • Place of Presentation: 筑波大学
  • Year and Date: 2010-08-11
• [Presentation] Obstacle problem of Navier-Stokes equations in thermohydraulics (2010)
  • Author(s): Takeshi Fukao
  • Organizer: AIMS' 8th International Conference on Dynamical Systems, Differential Equations and Applications
  • Place of Presentation: ドイツ・ドレスデン
  • Year and Date: 2010-05-25
• [Presentation] 温度依存制約条件を含むNavier-Stokes方程式の解の存在について (2010)
  • Author(s): 深尾武史
  • Organizer: 日本数学会2010年度年会
  • Place of Presentation: 慶應大学
  • Year and Date: 2010-03-26
• [Presentation] 流速の大きさの制約条件に対する変分不等式の可解性について (2010)
  • Author(s): 深尾武史
  • Organizer: 第36回発展方程式研究会
  • Place of Presentation: 中央大学
• [Presentation] 流れの制約条件に対する変分不等式 (2010)
  • Author(s): 深尾武史
  • Organizer: 日本数学会2010年度秋季総合分科会
  • Place of Presentation: 名古屋大学
• [Presentation] Obstacle problem of Navier-Stokes equations in thermohydraulics (2010)
  • Author(s): T. Fukao
  • Organizer: AIMS' 8th International Conference on Dynamical Systems, Differential Equations and Applications
  • Place of Presentation: TU Dresden, Germany
• [Presentation] 温度依存制約条件を含むNavier-Stokes方程式の解の存在について (2010)
  • Author(s): 深尾武史
  • Organizer: 日本数学会2010年度年会
  • Place of Presentation: 慶応大学
• [Presentation] Global attractor of double obstacles problem in thermohydraulics (2009)
  • Author(s): Takeshi Fukao, Masahiro Kubo
  • Organizer: Evolution Equations, Related Topics and Applications
  • Place of Presentation: ドイツミュンヘンヘルムホルツセンター
  • Year and Date: 2009-09-11
• [Presentation] Global attractor for double obstacle problems in thermohydraulics (2009)
  • Author(s): Takeshi Fukao, Masahiro Kubo
  • Organizer: 4th Polish-Japanese Days on Current advances in applied nonlinear analysis and mathematical modelling issues
  • Place of Presentation: ポーランドワルシャワマドラリン
  • Year and Date: 2009-05-21
• [Presentation] 温度依存制約条件を含むNavier-Stokes方程式の解の存在について (2009)
  • Author(s): 深尾武史
  • Organizer: 第35回発展方程式研究会
  • Place of Presentation: 中央大学
• [Presentation] ある障害物問題の時間局所・大域解と大域的アトラクターについて (2009)
  • Author(s): 深尾武史-久保雅弘
  • Organizer: 日本数学会2009年度秋季総合分科会
  • Place of Presentation: 大阪大学
• [Presentation] Global attractor of double obstacle problem in thermohydraulics (2009)
  • Author(s): T. Fukao-M. Kubo
  • Organizer: Evolution Equations, Related Topics and Applications
  • Place of Presentation: Munchen, Germany
• [Presentation] Global attractor for double obstacle problems in thermohydraulics (2009)
  • Author(s): T. Fukao-M. Kubo
  • Organizer: 4th Polish-Japanese Days on Current advances in applied nonlinear analysis and mathematical modelling issues
  • Place of Presentation: Madralin, Poland