Takeshi Fukao, Department of Mathematics, Kyoto University of Education

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Research

Research Subject and Activities

Mathematics

  • Nonlinear Analysis
  • Evolution Equation
  • Variational Inequality

Mathematics Education

  • Learning method of functions
  • Modelling

Research Activities

Articles

Recent 5 years

  1. P. Colli, T. Fukao, and H. Wu, On a transmission problem for equation and dynamic boundary condition of Cahn–Hilliard type with nonsmooth potentials, to appear in Math. Nachr.
  2. 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
  3. 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
  4. T. Fukao and T. Motoda, Abstract approach to degenerate parabolic equations with dynamic boundary conditions, Adv. Math. Sci. Appl., 27 (2018), 29–44.
  5. 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
  6. 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
  7. 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
  8. 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
  9. 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
  10. 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
  11. 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
  12. 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
  13. 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
  14. 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
  15. 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
  16. 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
  17. 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
  18. 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
  19. T. Fukao and N. Kenmochi, Abstract theory of variational inequalities with Lagrange multipliers and application to nonlinear PDEs, Math. Bohem., 139 (2014), 391–399.
  20. 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.
All articles

Books

Nonlinear Analysis in Interdisciplinary Sciences:
Modellings, Theory and Simulations

5th

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

The Fifth Polish-Japanese Days on "Nonlinear Analysis in Interdisciplinary Sciences: Modellings, Theory and Simulations".

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