Takeshi Fukao, Department of Mathematics, Kyoto University of Education

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

京都教育大学 教育学部 数学科 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

非線形解析学、応用数学、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

学内委員

学外委員(数学/数学教育関連)

その他

論文(過去5年間)

1. 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, to appear in Commun. Pure Appl. Anal. DOI: 10.3934/cpaa.2021181, arXiv
2. 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.
3. 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
4. T. Fukao, On a perturbed fast diffusion equation with dynamic boundary conditions, Adv. Math. Sci. Appl., 29 (2020), 365–392. arXiv
5. 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, 1--27. DOI: 10.1007/s00030-020-00654-8, arXiv
6. 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
7. 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
8. 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
9. T. Fukao and T. Motoda, Abstract approach to degenerate parabolic equations with dynamic boundary conditions, Adv. Math. Sci. Appl., 27 (2018), 29–44. arXiv
10. 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
11. 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
12. 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
13. 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
14. 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)
15. 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
16. 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
17. 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
18. 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

学内情報サイト

　京都教育大学、研究者総覧へのリンクです。

• 　研究者総覧 (京都教育大学)

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
• 　J-GLOBAL (科学技術振興機構)
• 　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

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。

H.M.

S.F.

S.F.

T.K.

D.I.