### Research Subject and Activities

#### Mathematics

- Nonlinear Analysis
- Evolution Equation
- Variational Inequality

#### Mathematics Education

- Learning method of functions
- Modelling

#### Research Activities

- My Citations (Google Scholar)
- Takeshi Fukao (Research Gate)
- Takeshi Fukao (ORCID)
- Fukao, Takeshi (zbMATH)
- Takeshi Fukao's articles on arXiv (arXiv)

### Articles

#### Recent 5 years

- 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.
- 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 - 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 - T. Fukao and T. Motoda,
Abstract approach to degenerate parabolic equations with dynamic boundary conditions,
Adv. Math. Sci. Appl.,
**27**(2018), 29–44. - 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 - 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 - 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 - 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 - 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 - 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 - 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 - 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 - 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 - 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 - 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 - 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 - 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 - 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 - T. Fukao and N. Kenmochi,
Abstract theory of variational inequalities with Lagrange multipliers and application to nonlinear PDEs,
Math. Bohem.,
**139**(2014), 391–399. - 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.

### Books

#### 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

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