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 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
  2. 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
  3. 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.
  4. 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
  5. T. Fukao, On a perturbed fast diffusion equation with dynamic boundary conditions, Adv. Math. Sci. Appl., 29 (2020), 365–392. arXiv
  6. 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
  7. 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
  8. 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
  9. 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
  10. T. Fukao and T. Motoda, Abstract approach to degenerate parabolic equations with dynamic boundary conditions, Adv. Math. Sci. Appl., 27 (2018), 29–44. arXiv
  11. 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
  12. 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
  13. 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
  14. 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
  15. 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)
  16. 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
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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