Partial differential equations of nonlinear diffusion in thermohydraulics and their applications

• Project/Area Number: 18740095
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Single-year Grants
• Research Field: Global analysis
• Research Institution: Gifu National College of Technology
• Principal Investigator: FUKAO Takeshi Gifu National College of Technology, 一般科目(自然), 講師 (00390469)
• Project Period (FY): 2007 – 2008
• Project Status: Completed (Fiscal Year 2008)
• Budget Amount: ¥3,310,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥210,000); Fiscal Year 2008: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000); Fiscal Year 2007: ¥800,000 (Direct Cost: ¥800,000); Fiscal Year 2006: ¥1,600,000 (Direct Cost: ¥1,600,000)
• Keywords: 非線形現象 / 発展方程式 / 熱水力学 / 非線形偏微分方程式系 / 可解性 / 変分不等式 / 非線形偏微分方程式 / 自由境界値問題 / フェイズフィールド方程式

Research Abstract

熱水力学に現れる放物型偏微分方程式の連立系に対する可解性に関する結果を得た。ナヴィエ・ストークス方程式と連立した非線形熱方程式として、第一に相転移現象を記述する様な拡散項に強い非線形性を持つある熱方程式との連立系に対して、3次元の場合に弱解の存在とそのための与えられた初期関数等の必要条件を得た。第二に、制約条件が非線形性として主要項にある熱方程式との連立系に対して、2次元の場合に弱解の存在と一意性、解の連続依存性の結果を得た。

Research Products

• [Journal Article] Time-dependent double obstacle problem in thermohydraulics, GAKUTO Internat (2008)
  • Author(s): T. Fukao and M. Kubo
  • Journal Title: Ser. Math. Appl Vol. 29 Pages: 73-92
  • Peer Reviewed
• [Journal Article] Free boundary problems of the nonlinear heat equations coupled with the Navier-Stokes equations (2008)
  • Author(s): T. Fukao
  • Journal Title: Recent Advances in Nonlinear Analysis Pages: 67-76
  • Peer Reviewed
• [Journal Article] Time-dependent double obstacle problem in thermohodraulics (2008)
  • Author(s): 深尾武史
  • Journal Title: GAKUTO Internat. Ser. Math. Appl. 29 Pages: 73-92
  • Peer Reviewed
• [Journal Article] Free boundary problems of the nonlinear heat equations coupled with the Navier-Stokes equations (2008)
  • Author(s): 深尾武史
  • Journal Title: Recent Advances in Nonlinear Analysis Pages: 67-76
  • Peer Reviewed
• [Journal Article] Nonlinear degenerate parabolic equations for a thermohydraulic model (2007)
  • Author(s): T. Fukao and M. Kubo
  • Journal Title: Discrete Contin. Dyn. Syst. Supplement Pages: 399-408
  • Peer Reviewed
• [Journal Article] Nonlinear degererate parabolic equations for a thermohydraulic model (2007)
  • Author(s): 深尾 武史
  • Journal Title: Discrete and continuous dynamical systems Pages: 399-408
  • Peer Reviewed
• [Journal Article] Embedding theorem for phase field equation with convection (2006)
  • Author(s): Takesi FUKAO
  • Journal Title: Free Boundary Problems : Theory and Applications Internat.Ser.Numer.Math. 154 Pages: 169-178
• [Journal Article] System of nonlinear heat equation and Navier-Stokes equations (2006)
  • Author(s): Takesi FUKAO
  • Journal Title: Mathematical Modeling and analysis for nonlinear phenomena, RIMS Kokyuroku 1522 Pages: 82-100
• [Journal Article] Partial differential equations for solid-liquid phase transition with fluid motion (2006)
  • Author(s): Takesi FUKAO
  • Journal Title: Mathematical Models of Phenomena and Evolution Equations, RIMS Kokyuroku 1475 Pages: 45-64
• [Journal Article] Time dependent nonlinear evolution equations and their applications (2006)
  • Author(s): Takesi FUKAO
  • Journal Title: Bull.Gifu National College of Technology 42 Pages: 15-24
  • NAID: 110006424329
• [Presentation] 熱水力学に現れる障害物問題の弱解と漸近挙動について (2008)
  • Author(s): 深尾武史-久保雅弘
  • Organizer: 第34回発展方程式研究会
  • Place of Presentation: 中央大学
• [Presentation] 熱水力学に現れる障害物問題について (2008)
  • Author(s): 深尾武史-久保雅弘
  • Organizer: 第30回発展方程式若手セミナー
  • Place of Presentation: 山梨県笛吹市
• [Presentation] Time dependent obstacle problems in thermohydraulics, AIMS' 7th International Conference on Dynamical Systems (2008)
  • Author(s): T. Fukao and M. Kubo
  • Organizer: Differential Equations and Applications
  • Place of Presentation: Texas, USA
• [Presentation] Time dependent obstacle problems in thermohydraulics (2008)
  • Author(s): 深尾武史
  • Organizer: AIMS' 7th International Conference on Dynamical Systems, Differential Equations and Applications
  • Place of Presentation: Texas, USA
• [Presentation] 熱水力学に現れるある変分不等式と解の正則性について (2008)
  • Author(s): 深尾 武史
  • Organizer: 日本数学会2008年度年会,
  • Place of Presentation: 近畿大学
• [Presentation] 移流項を含むある発展変分不等式の解の存在について (2007)
  • Author(s): 深尾武史-久保雅弘
  • Organizer: 第3回非線形数理科学
  • Place of Presentation: 千葉大学
• [Presentation] Abstract approach to the phase field equations with convection (2007)
  • Author(s): 深尾武史
  • Organizer: 日本数学会2007年度年会
  • Place of Presentation: 埼玉大学
• [Presentation] 移流項を含むある発展変分不等式の解の存在について (2007)
  • Author(s): 深尾 武史
  • Organizer: 第29回発展方程式若手セミナー
  • Place of Presentation: 山口市
• [Presentation] 熱水力学に現れる二重障害物問題の近似解について (2007)
  • Author(s): 深尾 武史
  • Organizer: 第3回非線形数理科学
  • Place of Presentation: 千葉大学
• [Presentation] ガレルキン法によるあるシステムの解の存在について (2006)
  • Author(s): 深尾武史
  • Organizer: 第2回非線形数理科学
  • Place of Presentation: 千葉大学
• [Presentation] Free boundary problem for phase field equations and Navier-Stokes equations without the Carman-Kozeny penalty (2006)
  • Author(s): T. Fukao
  • Organizer: International Conference on Nonlinear Analysis
  • Place of Presentation: Hsinchu, Taiwan
• [Presentation] Free boundary problem for phase field equations without the penalization term of Carman-Kozeny type (2006)
  • Author(s): 深尾武史
  • Organizer: 日本数学会2006年度秋季総合分科会
  • Place of Presentation: 大阪市立大学
• [Presentation] Carman-Kozeny処罰項がないNavier-Stokes方程式とフェイズフィールド方程式の自由境界問題について (2006)
  • Author(s): 深尾武史
  • Organizer: 第32回発展方程式研究会
  • Place of Presentation: 中央大学
• [Presentation] Nonlinear degenerate parabolic equations for a thermohydraulics model, AIMS' 6th International Conference on Dynamical Systems (2006)
  • Author(s): T. Fukao and M. Kubo
  • Organizer: Differential Equations and Applications
  • Place of Presentation: Poirtiers, France
• [Book] Dissipative phase transitions (Ser.Adv.Math.Appl.Sci. 第5章担当) (P.Colli, N.Kenmochi and J.Sprekels ed.) (2006)
  • Author(s): Takesi FUKAO
  • Total Pages: 13
  • Publisher: Weak solutions for Stefan problems with convections