Takeshi Fukao, Faculty of Advanced Science and Technology, Ryukoku University

名前

深尾　武史

学位

博士（理学）：千葉大学　2003年
修士（教育学）：岐阜大学　2000年

職位

龍谷大学 先端理工学部 数理・情報科学課程 教授

資格

* 小学校教諭第一種免許状
* 中学校教諭第一種免許状　[数学]
* 高等学校教諭第一種免許状　[数学]
* 小学校教諭専修免許状
* 中学校教諭専修免許状　[数学]
* 高等学校教諭専修免許状　[数学]
* （財）日本バスケットボール協会　JBA公認B級審判員
* （財）日本バスケットボール協会　JBA公認D級コーチ
* （財）日本バスケットボール協会　JBA公認3級審判インストラクター

研究分野

発展方程式、非線形解析学、数学教育

会員

日本数学会、 数学教育学会、 The International Society for the Interaction of Mechanics and Mathematics

学外委員(数学/数学教育関連)

その他

論文

1. T. Fukao, M. Ikeda, and S. Uchida, Heat equation on the hypergraph containing vertices with given data, J. Math. Anal. Appl., 540 (2024), Article number: 128675, 19 pp. DOI:10.1016/j.jmaa.2024.128675(open access)
2. M. Okumura and T. Fukao, Structure-preserving schemes for Cahn–Hilliard equations with dynamic boundary conditions, Discrete Contin. Dyn. Syst. Ser. S, 17 (2024), 362–394. DOI:10.3934/dcdss.2023207
3. T. Fukao and G. Schimperna, On the Cahn–Hilliard–Oono equation with singular potential and volume constraint, Discrete Contin. Dyn. Syst. Ser. S, 17 (2024), 285–303. DOI:10.3934/dcdss.2023198
4. Y. Akagawa, T. Fukao, and R. Kano, Time-dependence of the threshold function in the perfect plasticity model, Adv. Math. Sci. Appl., 32 (2023), 371–398.
5. P. Colli, T. Fukao, and L. Scarpa, A Cahn-Hilliard system with forward-backward dynamic boundary condition and non-smooth potentials, J. Evol. Equ., 22 (2022), Article number: 89, 31 pp. DOI:10.1007/s00028-022-00847-x, arXiv
6. P. Colli, T. Fukao, and L. Scarpa, The Cahn–Hilliard equation with forward-backward dynamic boundary condition via vanishing viscosity, SIAM J. Math. Anal., 54 (2022), 3292–3315. DOI:10.1137/21M142441X, arXiv
7. M. Okumura, T. Fukao, D. Furihata, and S. Yoshikawa, A second-order accurate structure-preserving scheme for the Cahn–Hilliard equation with a dynamic boundary condition, Commun. Pure Appl. Anal., 21 (2022), 355–392. DOI:10.3934/cpaa.2021181, arXiv
8. M. Okumura and T. Fukao, A new structure-preserving scheme with the staggered space mesh for the Cahn–Hilliard equation under a dynamic boundary condition, Adv. Math. Sci. Appl., 30 (2021), 347–376.
9. T. Fukao and H. Wu, Separation property and convergence to equilibrium for the equation and dynamic boundary condition of Cahn–Hilliard type with singular potential, Asymptotic Anal., 124 (2021), 303–341． DOI:10.3233/ASY-201646, arXiv
10. T. Fukao, On a perturbed fast diffusion equation with dynamic boundary conditions, Adv. Math. Sci. Appl., 29 (2020), 365–392. arXiv
11. P. Colli and T. Fukao, Vanishing diffusion in a dynamic boundary condition for the Cahn–Hilliard equation, NoDEA Nonlinear Differential Equations Appl., 27 (2020), Article number: 53, 27 pp. DOI:10.1007/s00030-020-00654-8, arXiv
12. P. Colli, T. Fukao, and H. Wu, On a transmission problem for equation and dynamic boundary condition of Cahn–Hilliard type with nonsmooth potentials, Math. Nachr., 293 (2020), 2051–2081. DOI:10.1002/mana.201900361(open access), arXiv
13. P. Colli and T. Fukao, Cahn–Hilliard equation on the boundary with bulk condition of Allen–Cahn type, Adv. Nonlinear Anal., 9 (2020), 16–38. DOI:10.1515/anona-2018-0055(open access), arXiv
14. P. Colli, T. Fukao, and K. F. Lam, On a coupled bulk–surface Allen–Cahn system with an affine linear transmission condition and its approximation by a Robin boundary condition, Nonlinear Anal., 184 (2019), 116–147. DOI:10.1016/j.na.2018.10.018, arXiv
15. T. Fukao and T. Motoda, Abstract approach to degenerate parabolic equations with dynamic boundary conditions, Adv. Math. Sci. Appl., 27 (2018), 29–44. arXiv
16. T. Fukao, S. Kurima, and T. Yokota, Nonlinear diffusion equations as asymptotic limits of Cahn–Hilliard systems on unbounded domains via Cauchy's criterion, Math. Methods Appl. Sci., 41 (2018), 2590–2601. DOI:10.1002/mma.4760, arXiv
17. T. Fukao and T. Motoda, Nonlinear diffusion equations with Robin boundary conditions as asymptotic limits of Cahn–Hilliard systems, J. Elliptic Parabol. Equ., 4 (2018), 271–291. DOI:10.1007/s41808-018-0018-1, arXiv
18. T. Fukao and N. Yamazaki, A boundary control problem for the equation and dynamic boundary condition of Cahn–Hilliard type, pp.255–280 in "Solvability, Regularity, Optimal Control of Boundary Value Problems for PDEs", Springer INdAM Series, Vol.22, Springer, Cham, 2017. DOI:10.1007/978-3-319-64489-9_10
19. T. Fukao, S. Yoshikawa, and S. Wada, Structure-preserving finite difference schemes for the Cahn–Hilliard equation with dynamic boundary conditions in the one-dimensional case, Commun. Pure Appl. Anal., 16 (2017), 1915–1938. DOI:10.3934/cpaa.2017093
20. T. Fukao, Y. Tsuzuki, and T. Yokota, Solvability of p-Laplacian parabolic equations with constraints coupled with Navier–Stokes equations in 3D domains by using largeness of p, Funkcial. Ekvac., 60 (2017), 1–20. DOI:10.1619/fesi.60.1(open access)
21. M. H. Farshbaf-Shaker, T. Fukao, and N. Yamazaki, Lagrange multiplier and singular limit of double-obstacle problems for the Allen–Cahn equation with constraint, Math. Methods Appl. Sci., 40 (2017), 5–21. DOI:10.1002/mma.3905
22. T. Fukao, Cahn–Hilliard approach to some degenerate parabolic equations with dynamic boundary conditions, pp.282–291 in "System Modeling and Optimization", IFIP Advances in Information and Communication Technology, Springer, 2016. DOI:10.1007/978-3-319-55795-3_26
23. T. Fukao, Convergence of Cahn–Hilliard systems to the Stefan problem with dynamic boundary conditions, Asymptot. Anal., 99 (2016), 1–21. DOI:10.3233/ASY-161373, arXiv
24. P. Colli and T. Fukao, Nonlinear diffusion equations as asymptotic limits of Cahn–Hilliard systems, J. Differential Equations, 260 (2016), 6930–6959. DOI:10.1016/j.jde.2016.01.032, arXiv
25. P. Colli and T. Fukao, The Allen–Cahn equation with dynamic boundary conditions and mass constraints, Math. Methods Appl. Sci., 38 (2015), 3950–3967. DOI:10.1002/mma.3329, arXiv
26. P. Colli and T. Fukao, Equation and dynamic boundary condition of Cahn–Hilliard type with singular potentials, Nonlinear Anal., 127 (2015), 413–433. DOI:10.1016/j.na.2015.07.011, arXiv
27. M. H. Farshbaf-Shaker, T. Fukao, and N. Yamazaki, Singular limit of Allen–Cahn equation with constraints and its Lagrange multiplier, pp.418–427 in "Dynamical Systems and Differential Equations, AIMS Proceedings, 2015", American Institute of Mathematical Sciences, 2015. DOI:10.3934/proc.2015.0418(open access)
28. P. Colli and T. Fukao, Cahn–Hilliard equation with dynamic boundary conditions and mass constraint on the boundary, J. Math. Anal. Appl., 429 (2015), 1190–1213. DOI:10.1016/j.jmaa.2015.04.057, arXiv
29. T. Fukao and N. Kenmochi, Quasi-variational inequality approach to heat convection problems with temperature dependent velocity constraint, Discrete Contin. Dyn. Syst., 35 (2015), 2523–2538. DOI:10.3934/dcds.2015.35.2523
30. T. Fukao and N. Kenmochi, Abstract theory of variational inequalities with Lagrange multipliers and application to nonlinear PDEs, Math. Bohem., 139 (2014), 391–399. DOI:10.21136/MB.2014.143864
31. T. Fukao and N. Kenmochi, A thermohydraulics model with temperature dependent constraint on velocity fields, Discrete Contin. Dyn. Syst. Ser. S, 7 (2014), 17–34. DOI:10.3934/dcdss.2014.7.17
32. T. Fukao and N. Kenmochi, Lagrange multipliers in variational inequalities for nonlinear operators of monotone type, Adv. Math. Sci. Appl., 23 (2013), 545–574.
33. T. Fukao and N. Kenmochi, Parabolic variational inequalities with weakly time-dependent constraint, Adv. Math. Sci. Appl., 23 (2013), 365–395.
34. T. Fukao, On a variational inequality of Bingham and Navier–Stokes type in three dimensional space, pp.57–71 in "Nonlinear Analysis in Interdisciplinary Sciences", GAKUTO Internat. Ser. Math. Sci. Appl., Vol.36, Gakkōtosho, Tokyo, 2013.
35. T. Fukao and N. Kenmochi, Abstract theory of variational inequality and Lagrange multipliers, pp.237–246 in "Discrete and Continuous Dynamical Systems, Supplement 2013", American Institute of Mathematical Sciences, 2013.
36. T. Fukao, Variational inequality for the Stokes equations with constraint, pp.437–446 in "Discrete and Continuous Dynamical Systems, Supplement 2011", American Institute of Mathematical Sciences, 2011.
37. T. Fukao and N. Kenmochi, Variational inequality for the Navier–Stokes equations with time-dependent constraint, pp.87–102 in "International Symposium on Computational Science", GAKUTO Internat. Ser. Math. Sci. Appl., Vol.34, Gakkōtosho, Tokyo, 2011.
38. T. Fukao and M. Kubo, Global attractor of double obstacle problem in thermohydraulics, pp.87–102 in "Current Advances in Nonlinear Analysis and Related Topics", GAKUTO Internat. Ser. Math. Sci. Appl., Vol.32, Gakkōtosho, Tokyo, 2010.
39. T. Fukao and M. Kubo, Time-dependent obstacle problem in thermohydraulics, pp.240–249 in "Discrete and Continuous Dynamical Systems, Supplement 2009", American Institute of Mathematical Sciences, 2009.
40. T. Fukao and M. Kubo, Time-dependent double obstacle problem in thermohydraulics, pp.73–92 in "Nonlinear Phenomena with Energy Dissipation, Mathematical Analysis, Modeling and Simulation", GAKUTO Internat. Ser. Math. Sci. Appl., Vol.29, Gakkōtosho, Tokyo, 2008.
41. T. Fukao, Free boundary problems of the nonlinear heat equations coupled with the Navier-Stokes equations, pp.67–76 in "Recent Advances in Nonlinear Analysis, Proceedings of the International Conference on Nonlinear Analysis", World Scientific Publishing, 2008.
42. T. Fukao and M. Kubo, Nonlinear degenerate parabolic equations for a thermohydraulic model, pp.399–408 in "Discrete and Continuous Dynamical Systems, Supplement 2007", American Institute of Mathematical Sciences, 2007.
43. T. Fukao, Embedding theorem for phase field equation with convection, pp.169–178 in "Free Boundary Problems. Theory and Applications", International Series of Numerical Mathematics, Vol.154, Birkhäuser Verlag, 2006.
44. T. Fukao, Phase field equations with convections in non-cylindrical domains, pp.42–54 in "Mathematical Approach to Nonlinear Phenomena; Modelling, Analysis and Simulations", GAKUTO Internat. Ser. Math. Sci. Appl., Vol.23, Gakkōtosho, Tokyo, 2005.
45. T. Fukao and N. Kenmochi, Stefan problems with convection governed by Navier-Stokes equations, Adv. Math. Sci. Appl., 15 (2005), 29–48.
46. T. Fukao and N. Kenmochi, Degenerate parabolic equations with convection in non-cylindrical domains, Adv. Math. Sci. Appl., 14 (2004), 139–150.
47. M. Aso, T. Fukao, and N. Kenmochi, A new class of doubly nonlinear evolution equations, Taiwanese J. Math., 8 (2004), 103–124.
48. T. Fukao, Weak solutions for Stefan problems with convection in non-cylindrical domains, pp.28–47 in "Nonlinear Partial Differential Equations and Their Applications", GAKUTO Internat. Ser. Math. Sci. Appl., Vol.20, Gakkōtosho, Tokyo, 2004.
49. T. Fukao, N. Kenmochi, and I. Pawłow, Transmission-Stefan problems arising in Czochralski process of crystal growth, pp.151–165 in "Free Boundary Problems. Theory and Applications", International Series of Numerical Mathematics, Vol.147, Birkhäuser Verlag, 2003.
50. T. Fukao, Transmission problems for degenerate parabolic equations, pp.103–112 in "Elliptic and Parabolic Problems", World Scientific Publishing, 2002.
51. T. Fukao, N. Kenmochi, and I. Pawłow, Transmission problems arising in Czochralski process of crystal growth, pp.228–243 in "Mathematical Approach to Nonlinear Phenomena; Modelling, Analysis and Simulations", GAKUTO Internat. Ser. Math. Sci. Appl., Vol.17, Gakkōtosho, Tokyo, 2002.

学外情報サイト

　それぞれの団体が作成する研究業績情報サイトへのリンクです。

• 　Google Scholar
• 　Research Gate
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• 　research map (科学技術振興機構)
• 　ORCID (ORCID iD / 0000-0003-4899-6890)
• 　Publons (Web of Science ResearcherID / R-6245-2019)
• 　Scopus (Scopus Author ID / 55747452500)
• 　zbMATH
• 　arXiv

中等数学科教育の理論と実践

二澤 善紀 編著
ミネルヴァ書房 (2022)
ISBN: 9784623094080

　中学校・高等学校の数学科教員を目指す学生、すでに教壇に立つ教員を対象とした数学科教育法の教科書である。 各分野の教育内容に関する章は、数学理論と数学教育の研究者が協力し、また学習指導案作成などの実践的な章は現職教員が加わり執筆している。 小学校から高等学校までに扱う内容・領域の系統性を俯瞰できるよう整理して示し、数学教育の現状と課題をわかりやすく解説した。 各分野は、内容構成、学習指導、数学的背景からなり、数学科教員に必要な素養が身につく。

［ここがポイント］
◎ 中学校・高等学校の学習指導要領に対応
◎ 小学校から高等学校までに扱う内容・領域の系統性を俯瞰できる
◎ 各分野は、内容構成、学習指導、数学的背景からなる
◎ 数学科教員に必要な素養が身につくよう工夫
(出版社説明文より引用)

　第3章 関数 3.関数分野における数学的背景、 第5章 微分積分 3.微分積分分野における数学的背景、 第8章 集合と命題 3.集合論の数学的背景、を担当しました。

Solvability, Regularity, and Optimal Control of Boundary Value Problems for PDEs
In Honour of Prof. Gianni Gilardi

P. Colli, A. Favini, E. Rocca, G. Schimperna and J. Sprekels ed.
Springer INdAM Series, Volume 22
Springer, Cham (2017)
ISBN: 978-3-319-64488-2

This volume gathers contributions in the field of partial differential equations, with a focus on mathematical models in phase transitions, complex fluids and thermomechanics. These contributions are dedicated to Professor Gianni Gilardi on the occasion of his 70th birthday. It particularly develops the following thematic areas: nonlinear dynamic and stationary equations; well-posedness of initial and boundary value problems for systems of PDEs; regularity properties for the solutions; optimal control problems and optimality conditions; feedback stabilization and stability results. Most of the articles are presented in a self-contained manner, and describe new achievements and/or the state of the art in their line of research, providing interested readers with an overview of recent advances and future research directions in PDEs.. (出版社説明文より引用)

　第10章 A Boundary Control Problem for the Equation and Dynamic Boundary Condition of Cahn–Hilliard Type を神奈川大学 山崎教昭教授との共著として担当しました。

Nonlinear Analysis in Interdisciplinary Sciences:
Modellings, Theory and Simulations

T. Aiki, T. Fukao, N. Kenmochi, M. Niezgódka, M. Ôtani ed.
GAKUTO International Series.
Mathematical Sciences and Applications, Volume36
Gakkotosho (2013)
ISBN: 9784762504617

　2013年11月に開催されました国際会議 The Fifth Polish-Japanese Days on "Nonlinear Analysis in Interdisciplinary Sciences: Modellings, Theory and Simulations"の報告集が出版されました。
　

Dissipative Phase Transitions

P. Colli, N. Kenmochi, J. Sprekels ed.
Series on Advances in Mathematics for Applied Sciences, Volume 71
World Scientific (2006)
ISBN: 9789812566508

Phase transition phenomena arise in a variety of relevant real world situations, such as melting and freezing in a solid-liquid system, evaporation, solid-solid phase transitions in shape memory alloys, combustion, crystal growth, damage in elastic materials, glass formation, phase transitions in polymers, and plasticity. The practical interest of such phenomenology is evident and has deeply influenced the technological development of our society, stimulating intense mathematical research in this area. This book analyzes and approximates some models and related partial differential equation problems that involve phase transitions in different contexts and include dissipation effects. (出版社説明文より引用)

　第5章 Weak solutions for Stefan problems with convections を担当しました。

京都教育大学広報誌 第125号

　「鋸（のこぎり）は、たいてい引く方向に刃がついていて、押すときでなく引くときに切れるんだよ」 「金槌（かなづち）は、柄の先の方を持って振ることで、より大きな力で釘が打てるんだよ」と丁寧に道具の解説をされれば、「へーっ」と思うこともあります。 しかし、鋸や金槌を目の前にして、その仕組みや便利さの解説を聞くだけではなんだか物足りません。 実際に道具を使って木を切ってみたり、釘を打ってみたくなるものです。 使い方を知ることで、それまで無関心だった道具の仕組みや便利さにも興味がわくこともあります。 すでに仕組みや便利さに興味を持っていた人にとっても、使い方を知ればさらに理解も深まりますし、そもそも道具の便利さを知るには道具を使ってみるのが一番です。 さて、中学校や高校のあの教科を思い出すと、確かに内容は洗練、体系立てられていて、教科書ではその仕組みが丁寧に解説されていました。理屈抜きに「美しい」「すばらしい」と思った定理もたくさんあります。 しかし、道具としての使い方は全然体験できず便利だと思ったことはありませんでした。 試験の問題を解くためにあるとすら感じていたときもありました。 あの教科の楽しさを伝えるとき、「美しい」「すばらしい」という側面を見せるだけでなく、現象解明の「道具」としての使い方も体験させられるように工夫したいと考えています。

H.M.

S.F.

S.F.

T.K.

D.I.