AIKI Toyohiko

アイキトヨヒコ | AIKI Toyohiko

Affiliation and department：
Homepage URL (1)： http://mcm-www.jwu.ac.jp/~aikit/aiki.html

Research keywords (1)： Nonlinear partial differential equations

Research theme for competitive and other funds (27)：

2022 - 2025 弾性体に対する障害物問題の解析とその数値解法について
2019 - 2023 非均質領域における偏微分方程式の解析
2017 - 2021 Partial differential equations with the total mass conservation and related topics of abstract approach
2015 - 2018 Analysis for multi-scale models describing nonlinear phenomena in porous media
2012 - 2015 On development of analytical method for mathematical models including hysteresis and study of the suitability of the models

2011 - 2013 Plans of classes of mathematical activities based on skills of making goods

2008 - 2010 Mathematical modeling for a nonlinear phenomena appearing engineering field and its analysis

2008 - 2009 数学をコアとした探求型科学教育学習プログラムの開発と教員養成

2006 - 2009 Studies on dynamical systems of nonlinear phenomena with energy dissipation and the theory of stability

2006 - 2008 Analyses of function spaces of solutions of a parabolic equation and operators on these spaces

2005 - 2006 非線形解析学の新展開と科学教育学習プログラムの開発

2005 - 2006 数理科学的立場からの数学教材の開発・実践及び授業ビデオ作成

2004 - 2006 Analysis of a non-linear phenomenon mainly on the issue of shape-memory alloy

2004 - 2006 New development of convective reaction-diffusion systems and validation of numerical computation

2001 - 2004 Research on the structure and stability of the dynamical system describing phase transition phenomena

2002 - 2003 Analysis of nonlinear phenomena describing hysteresis operators

2002 - 2003 Study of integral operators on function spaces.

2000 - 2003 RESEARCH ON COMPLEX ANALYSIS BY GROUP THEORETIC AND GEOMETRIC METHOD

2000 - 2001 A research on a system of nonlinear partial differential equations describing phase transition phenomena

1999 - 2000 Study on phase transition problems with nonlinear control devices

1999 - 2000 Modelling and analysis of nonlinear phenomena with phase transitions

1998 - 1999 STUDIES ON MODULAR FORMS, NUMBER THEORY AND ALGEBRAIC STRUCTURES

1997 - 1998 Research on Complex Analytic Properties of Complex Homogeneous Spaces

1997 - 1998 Mathematical Research of Nonlinear Phenomena with Phase Transitions

1996 - 1996 非線形偏微分方程式のシステムの関数解析的手法による研究

1995 - 1995 複素等質空間の関数論的性質の研究

Analysis of concrete carbonation process

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Papers (66)：

Chiharu Kosugi, Toyohiko Aiki. Large time behavior of solutions for a PDE model for compressible elastic curve. Discrete and Continuous Dynamical Systems - S. 2023
Toyohiko Aiki, Kota Kumazaki, Adrian Muntean. A free boundary problem describing migration into rubbers - Quest for the large time behavior. ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik. 2022
Toyohiko Aiki, Miyu Hotta. Age-dependent model for population dynamics of polyps, one life stage of jellyfish. Advances in Mathematical Sciences and Applications. 2022. 31. 2. 473-480
Kota Kumazaki, Toyohiko Aiki, Adrian Muntean. Local existence of a solution to a free boundary problem describing migration into rubber with a breaking effect. Networks and Heterogeneous Media. 2022. 18. 1. 80-108
Toyohiko Aiki, Nils Kröger, Adrian Muntean. A macro-micro elasticity-diffusion system modeling absorption-induced swelling in rubber foams: Proof of the strong solvability. Quarterly of Applied Mathematics. 2021. 79. 3. 545-579

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MISC (5)：

Adrian Muntean, Toyohiko Aiki. PREFACE TO "THE MATHEMATICS OF CONCRETE". NETWORKS AND HETEROGENEOUS MEDIA. 2014. 9. 4. I-II
Toyohiko Aiki, Joost Hulshof, Noboyuki Kenmochi, Adrian Muntean. ANALYSIS OF NON-EQUILIBRIUM EVOLUTION PROBLEMS: SELECTED TOPICS IN MATERIAL AND LIFE SCIENCES. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S. 2014. 7. 1. I-III
On information science education for students belonging to mathematics course in university : Analysis for correlation coefficients between scores of exams of mathematics and programing. 2014. 55. 3. 89-97
Aiki Toyohiko, Murase Yusuke, Sato Naoki, Shirakawa Ken. A mathematical model for a hysteresis appearing in adsorption phenomena (New developments of the theory of evolution equations in the analysis of non-equilibria). RIMS Kokyuroku. 2013. 1856. 1-11
愛木豊彦. 図形領域における数学的活動を取り入れた教材の開発と実践. 2007, 第11回数学教育学会大学院生部会発表論文集. 2007. 1-4

Books (14)：

Models for shape memory alloys described by subdifferentials of indicator functions
Elliptic and Parabolic problems, Rolduc and Gaeta 2001, World Scientific Publishing 2002
On one-phase Stefan problems for sublinear heat equations
Proceedings of the Third Asian Mathematical Conference 2000, World Scientific Publishing 2002
Some models for shape memory alloys
Mathematical Aspects of Modelling Structure Formation Phenomena 2001
Stefan problems for semilinear parabolic eqnations with Dirichlet boundary conditions
Free boundary problems, Theory and Applications (]G0002[) 2000
Stefan problems with dynamic boundary condition in cluding the hysteresis operator
Free boundary problems, Theory and Applications (]G0001[) 2000

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Lectures and oral presentations (8)：

Recent results related to the two-scale model for concrete carbonation
(The 11th AIMS conference on dynamical systems, differential equations and applications 2016)
Continuous dependence of solutions to the free boundary problem describing adsorption phenomena on boundary data
(Equadiff 2015 2015)
Large time behavior of a solution to a free boundary problem describing adsorption phenomenum
(10th AIMS international conference on dynamical systems, differential equations and applications 2014)
Examples of application of mathematics learning at junior high school
(The Sixth International Conference on Science and Mathematics Education in Developing Countries 2013)
Large time behavior of a solution to a two-scale problem as mathematical model for sulfate attack in sewer pipes
(Equadiff13 2013)

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Education (2)：

Professional career (2)：

Association Membership(s) (4)：

日本数学教育学会 , 数学教育学会 , 応用数理学会 , 日本数学会

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