AIKI, Toyohiko
Postal
address
Department of Mathematics
Faculty of Education
Gifu
University
Yanagido 1-1, Gifu, 501-1193
JAPAN
Email aiki@gifu-u.ac.jp
Journal of Editors
・
Advances in Mathematical Sciences and Applications
・
DCDS-S
Publications
Mathematics
Mathematical
Education(数学教育)
AIKI, Toyohiko
A free boundary problem for an elastic material
Dynamical Systems, Differential Equations and Applications, supplement 2007.
American Institute of Mathematical Sciences, (2007)10-17
AIKI, Toyohiko; Okazaki, Takanobu
One-dimensional shape memory alloy problem with Duhem type of hysteresis operator
Free boundary problems, Theory and applications,
International Series of Numerical Mathematics,
Vol. 154, 2006, 1-9
AIKI, Toyohiko; Emil Minchev ; Okazaki, Takanobu
Mathematical models for phase change problems with hysteresis effect
Proceedings of the Fourth World Congress of Nonlinear Analysts, Orlando, Florida, June 30-July 7, 2004, Elsevier, (2006)e1185-e1198
AIKI, Toyohiko
Phase-field model including a hysteresis operator
Proceedings of the Fourth World Congress of Nonlinear Analysts, Orlando, Florida, June 30-July 7, 2004, Elsevier, (2006)e1219-e1230
AIKI, Toyohiko; Kadaoya,
Atsushi; Yoshikawa, Shuji
One-dimensional shape memory alloy
problem with small viscosity
Mathematical Approach to Nonlinear Phenomena;
Modeling, Analysis and Simulations,
Gakuto International Series,
Mathematical Sciences and Applications,Vol. 23, 2005, 1-8
AIKI, Toyohiko; Emil Minchev
A Prey - Predator Model with
Hysteresis Effect
SIAM Journal on Mathematical Analysis, Vol. 36, (2005)2020-2032
AIKI,
Toyohiko
A model
of 3D shape memory alloy materials
Journal of the Mathematical Society of Japan, Vol.
57, (2005)903-933
AIKI, Toyohiko;
Karl-Heinz HOFFMANN; OKAZAKI, Takanobu
Wellposedness for a new
mathematical model for magnetostrictive thin film multilayers
Advances in Mathematical Sciences and Applications,
Vol. 14, (2004)417-442
AIKI, Toyohiko;
Imai, Hitoshi ;
Ishimura, Naoyuki ; Yamada, Yoshio
One-phase Stefan problems for sublinear
heat equations: Asymptotic behavior of solutions
Communications in Applied Analysis, Vol. 8,
(2004)1-15
AIKI, Toyohiko
One-dimensional shape memory alloy
problems including a hysteresis operator
Funkcialaj
Ekvaccioj, Vol. 46, (2003)441-469
AIKI, Toyohiko; Kenmochi, Nobuyuki
Models for shape memory alloys
described by subdifferentials of indicator functions
Elliptic and
Parabolic Problems, Rolduc and Gaeta 2001, World Scientific Publishing, 2002,
pp. 1-10
AIKI, Toyohiko; Imai, Hitoshi; Ishimura, Naoyuki; Yamada, Yoshio
Well-posedness of one-phase Stefan problems for sublinear heat equations
Journal of Nonlinear Analysis, Vol. 51, (2002)587-606
AIKI, Toyohiko; Imai, Hitoshi; Ishimura, Naoyuki; Yamada, Yoshio
On one-phase Stefan problems for sublinear heat equations
Proceedings of the Third Asian Mathematical Conference 2000, World
Scientific Publishing, 2002, pp. 6-11
AIKI, Toyohiko
Uniqueness for multi-dimensional Stefan problems
with nonlinear boundary conditions described by maximal monotone operators
Differential and Integral Equations, Vol. 15, (2002)973-1008
AIKI, Toyohiko; Kenmochi, Nobuyuki
Some models for shape memory
alloys
Mathematical Aspects of Modelling Structure Formation Phenomena,
Gakuto International Series, Mathematical Sciences and Applications, Vol. 17,
2001, 144-162
AIKI, Toyohiko; Imai, Hitoshi ; Takeuchi, Toshiki ; Schewli Shamim
Shanta ; Ishimura Naoyuki
Numerical computation of Lyapunov exponents related
to attractors in a free boundary problem
Nonlinear Analysis, Vol. 47,
(2001)3823-3833
AIKI, Toyohiok; Kadoya, Atsushi; Sato, Naoki
Optimal control
problem for phase-field equations with nonlinear dynamic boundary conditions
Nonlinear Analysis, Vol. 47, (2001) 3183-3194
AIKI, Toyohiko; Kenmochi, Nobuyuki
Some models for
shape memory alloys,
自由境界問題, 2001, 数理解析研究所講究録, No.
1210, 167-178
AIKI, Toyohiko; IMAI, Hitoshi
Stability of
global solutions to one phase Stefan problems for a semilinear parabolic
equation,
Czechoslovak Mathematical Journal, 50(125),
135-153(2000)
AIKI, Toyohiko; SATO, Naoki
Stefan problems
with dynamic boundary condition including the hysteresis operator,
Proceedins of International conference on:
Free boundary
problems, Theory and Applications I,
Gakuto International Series,
Mathematical Sciences and Applications,
Vol. 13, 2000, 1-10
IMAI, Hitoshi; Ishimura, Naoyuki; AIKI, Toyohiko
Analysis on one-phase
Stefan problems for semilinear
parabolic equations with Dirichlet boundary conditions,
Proceedins of International conference on:
Free boundary
problems, Theory and Applications II,
Gakuto International Series,
Mathematical Sciences and Applications,
Vol. 14, 2000, 176-183
AIKI, Toyohiko
Weak solutions for Falk's model of
shape memory alloys.
Mathematical Methods in the Applied
Sciences, 23, 299-319 (2000).
Aiki, Toyohiko; Imai, Hitoshi
Global existence of
solutions to one-phase Stefan problems for semilinear parabolic
equations.
Annali di Matematica pura ed applicata, 175, No. 4,
327-337(1998).
AIKI, Toyohiko
Global attractors for two-pahse
Stefan problems in one-dimensional space.
Abstract and Applied
Analysis, 2, No. 1-2, 47-66(1997).
Sato, Naoki; Aiki, Toyohiko
$\omega$-limit sets for solution of phase field equations with
constraints under nonlinear dynamic boundary conditions.
Nishiura, Y. (ed.) et al., Proceedings of the international conference on
asymptotics in nonlinear diffusive systems -- towards the understanding of
singularities in dissipative structures --, Sendai, Japan, July 28--August 1,
1997. Sendai: Tohoku Univ. Tohoku Math. Publ. 8, 253-256 (1998).
Aiki, Toyohiko
Blow-up points to one phase Stefan
problems with Dirichlet boundary conditions.
Malanowski,
Kazimierz (ed.) et al., Modelling and optimization of distributed parameter
systems. Applications to engineering. Papers from the IFIP WG 7.2 conference
held in Warsaw (Poland), July 17--21, 1995. London: Chapman \& Hall. 83-89
(1996).
Aiki, T.; Imai, H.
Behaviour of blow-up solutions
to one-phase Stefan problems with Dirichlet boundary conditions.
Niezgodka, Marek (ed.) et al., Free boundary problems, theory and
applications. Lectures presented at the congress, Zakopane, Poland, June 11--18,
1995. Harlow: Longman. Pitman Res. Notes Math. Ser. 363, 3-15 (1996).
Aiki, Toyohiko
Behavior of free boundaries of
blow-up solutions to one-phase Stefan problems.
Nonlinear Anal.,
Theory Methods Appl. 26, No.4, 707-723 (1996). [ISSN 0362-546X]
Aiki, Toyohiko
Periodic stability of solutions to
some degenerate parabolic equations with dynamic boundary conditions.
J. Math. Soc. Japan 48, No.1, 37-59 (1996).
Aiki, Toyohiko
Stefan problems in several space
variables with dynamic boundary conditions.
Lakshmikantham, V.
(ed.), World congress of nonlinear analysts '92. Proceedings of the first world
congress, Tampa, FL, USA, August 19-26, 1992. 4 volumes. Berlin: de Gruyter.
281-289 (1996).
Aiki, Toyohiko
Multi-dimensional two-phase Stefan
problems with nonlinear dynamic boundary conditions.
Kenmochi, N.
(ed.) et al., Proceedings of the Banach Center minisemester on nonlinear
analysis and applications, Warsaw, Poland, November 14 -- December 15, 1994.
Tokyo: Gakkotosho Co., Ltd. GAKUTO Int. Ser., Math. Sci. Appl. 7, 1-25
(1995).
Aiki, Toyohiko
Periodic solutions to some
degenerate parabolic equations with nonlinear dynamic boundary
conditions.
Sci. Rep. Fac. Educ., Gifu Univ., Nat. Sci. 20, No.1,
35-59 (1995).
Aiki, Toyohiko
Multi-dimensional Stefan problems
with dynamic boundary conditions.
Appl. Anal. 56, No.1-2, 71-94
(1995).
Aiki, Toyohiko
Periodic solutions for multi-phase
Stefan problems with dynamic boundary conditions.
Bainov, D.
(ed.) et al., Proceedings of the fourth international colloquium on differential
equations, Plovdiv, Bulgaria, August 18-22, 1993. Utrecht: VSP. 3-9 (1994).
Aiki, Toyohiko
Behavior of solutions to
one-dimensional two-phase Stefan problems with dynamic boundary
conditions.
Kawarada, H. (ed.) et al., Proceedings of the
international conference on nonlinear mathematical problems in industry, held at
Iwaki Meisei University, Iwaki, Japan, during Nov. 9-13, 1992. II. Tokyo:
Gakkotosho, GAKUTO Int. Ser., Math. Sci. Appl. 2, 547-570 (1993).
Aiki, Toyohiko
Solvabilities of nonlinear
elliptic-parabolic equations with dynamic boundary conditions.
Sci. Rep. Fac. Educ., Gifu Univ., Nat. Sci. 18, No.2, 35-54
(1994).
Aiki, Toyohiko
Periodic stability of solutions to
two-phase Stefan problems with nonlinear boundary condition.
Nonlinear Anal., Theory Methods Appl. 22, No.12, 1445-1474 (1994).
Aiki, T.; Kenmochi, N.; Shinoda, J.
Periodic
stability for Stefan problems with flux boundary conditions.
Chadam, John M. (ed.) et al., Free boundary problems involving solids.
Proceedings of the international colloquium "Free boundary problems: theory and
applications", held in Montreal, Canada, June 13 - June 22, 1990. Harlow, Essex:
Longman Scientific \& Technical, Pitman Res. Notes Math. Ser. 281, 158-163
(1993).
Aiki, Toyohiko
Two-phase Stefan problems with
dynamic boundary conditions.
Adv. Math. Sci. Appl. 2, No.2,
253-270 (1993).
Aiki, Toyohiko; Shinoda, Junichi; Kenmochi, Nobuyuki
Periodic stability for some degenerate parabolic equations with
nonlinear flux conditions.
Nonlinear Anal., Theory Methods Appl.
17, No.9, 885-902 (1991).
Aiki, Toyohiko; Kenmochi, Nobuyuki
Behavior of
solutions to two-phase Stefan problems for nonlinear parabolic
equations.
Bull. Fac. Educ., Chiba Univ., Part 2 39, 15-62
(1991).
Aiki, Toyohiko
The existence of solutions of
two-phase Stefan problems for nonlinear parabolic equations.
Control Cybern. 19, No.1/2, 41-62 (1990).
Aiki, Toyohiko
Two-phase Stefan problems for
parabolic-elliptic equations.
Proc. Japan Acad., Ser. A 64,
No.10, 377-380 (1988).
数学教育
村岡恵理
数学的活動を取り入れた発展的・総合的な教材の提案
数学教育学会誌臨時増刊、2003年度数学教育学会春季年会発表論文集、64-66
岩崎美奈
現象の数理的考察にもとづく発展的学習教材の提案
数学教育学会誌臨時増刊、2003年度数学教育学会春季年会発表論文集、61-63
岩崎美奈
身近な現象を新しい視点からとらえた教材の提案
岐阜数学教育研究，第１号, 64-74
岩崎美奈
数理的考察のよさを味わう教材の提案ーてこを用いた授業実践報告ー
岐阜数学教育研究，第１号, 54-63
近藤法和，林英里奈
算数教育に対する現職教員の意識調査
岐阜数学教育研究，第１号, 11-13
村岡恵理
算数的活動をもとにした「総合的な学習時間」教材の実践
数学教育学会誌研究紀要臨時増刊、2002年度数学教育学会秋季例会発表論文集、29-31
林英里奈
算数教育に対する児童の意識調査と分析ー算数離れを生み出す原因を探るー
岐阜大学カリキュラム開発センター研究報告, Vol.
21(2002)21-28
算数・数学教材開発の今後の方向について
岐阜大学カリキュラム開発センター研究報告, Vol. 21(2002)1-8
井上春奈,
近藤法和
数理モデルを構成する授業実践
数学教育学会誌研究紀要臨時増刊、2002年度数学教育学会春季年会発表論文集、4-6
近藤法和,
井上春奈
実験を中心とする「総合的な学習の時間」教材の提案
数学教育学会誌研究紀要臨時増刊、2002年度数学教育学会春季年会発表論文集、1-3
井上春奈, 近藤法和,
山田雅博
情報機器を活用した小学校での授業実践
数学教育学会誌研究紀要臨時増刊、2001年度数学教育学会秋季例会発表論文集、154-156
近藤法和, 井上春奈,
山田雅博
数理的な考え方を養う授業実践（お線香と扇風機による実験）
数学教育学会誌研究紀要臨時増刊、2001年度数学教育学会秋季例会発表論文集、151-153
山田雅博
教育学部における卒業研究のあり方に関する一提案
数学教育学会研究紀要臨時増刊、2001年度数学教育学会春季年会発表論文集、118-120
板垣由佳、剣持信幸
総合学習教材の開発を目指した面積学習の導入例
数学教育学会研究紀要臨時増刊、2001年度数学教育学会春季年会発表論文集、10-12
数学が嫌いな子ども達の増加にどう対処するか
中学校数学の研究、大日本図書、2001年1学期号,1