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

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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

Peer-reviewed articles

  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.

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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