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## Aiki, Toyohiko

Compute Distance To:
 Author ID: aiki.toyohiko Published as: Aiki, T.; Aiki, Toyohiko
 Documents Indexed: 84 Publications since 1988, including 3 Books
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#### Co-Authors

 28 single-authored 13 Muntean, Adrian 10 Imai, Hitoshi 10 Kenmochi, Nobuyuki 9 Sato, Naoki 6 Ishimura, Naoyuki 5 Timoshin, Sergey A. 4 Yamada, Yoshio 3 Kadoya, Atsushi 3 Kumazaki, Kota 3 Murase, Yusuke 3 Niezgódka, Marek 3 Okazaki, Takanobu 3 Ôtani, Mitsuharu 2 Minchev, Emil 2 Shinoda, Junichi 1 Anthonissen, Martijn Johannes Hermanus 1 Fatima, Tasnim 1 Fukao, Takeshi 1 Hoffmann, Karl-Heinz 1 Hulshof, Joost 1 Kopfová, Jana 1 Krehel, Oleh 1 Shanta, Shewli Shamim 1 Shirakawa, Ken 1 Takeuchi, Toshiki 1 Yoshikawa, Shuji
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#### Serials

 7 Advances in Mathematical Sciences and Applications 6 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 4 Networks and Heterogeneous Media 4 Discrete and Continuous Dynamical Systems. Series S 3 Communications in Applied Analysis 3 RIMS Kokyuroku 3 GAKUTO International Series. Mathematical Sciences and Applications 3 Nonlinear Analysis. Theory, Methods & Applications 2 Applicable Analysis 2 Journal of Mathematical Analysis and Applications 2 Mathematical Methods in the Applied Sciences 2 Journal of the Mathematical Society of Japan 2 SIAM Journal on Control and Optimization 2 Science Report of the Faculty of Education. Natural Science 2 Discrete and Continuous Dynamical Systems 1 Annali di Matematica Pura ed Applicata. Serie Quarta 1 Control and Cybernetics 1 Czechoslovak Mathematical Journal 1 Funkcialaj Ekvacioj. Serio Internacia 1 Journal of Differential Equations 1 Proceedings of the Japan Academy. Series A 1 Systems & Control Letters 1 Differential and Integral Equations 1 SIAM Journal on Mathematical Analysis 1 Abstract and Applied Analysis 1 Interfaces and Free Boundaries 1 Nonlinear Analysis. Real World Applications 1 Communications on Pure and Applied Analysis 1 Izvestiya Irkutskogo Gosudarstvennogo Universiteta. Seriya Matematika
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#### Fields

 77 Partial differential equations (35-XX) 23 Mechanics of deformable solids (74-XX) 18 Classical thermodynamics, heat transfer (80-XX) 11 Operator theory (47-XX) 6 Calculus of variations and optimal control; optimization (49-XX) 6 Fluid mechanics (76-XX) 6 Biology and other natural sciences (92-XX) 5 General and overarching topics; collections (00-XX) 3 Numerical analysis (65-XX) 3 Statistical mechanics, structure of matter (82-XX) 3 Systems theory; control (93-XX) 2 Dynamical systems and ergodic theory (37-XX) 1 History and biography (01-XX) 1 Ordinary differential equations (34-XX) 1 Functional analysis (46-XX)

#### Citations contained in zbMATH Open

45 Publications have been cited 171 times in 88 Documents Cited by Year
A prey-predator model with hysteresis effect. Zbl 1086.35154
Aiki, Toyohiko; Minchev, Emil
2005
A free-boundary problem for concrete carbonation: front nucleation and rigorous justification of the $$\sqrt{{t}}$$-law of propagation. Zbl 1276.35127
2013
Well-posedness of a mathematical model for moisture transport appearing in concrete carbonation process. Zbl 1282.35186
Aiki, Toyohiko; Kumazaki, Kota
2011
Large time behavior of solutions to a moving-interface problem modeling concrete carbonation. Zbl 1202.35362
2010
Homogenization of a thermo-diffusion system with Smoluchowski interactions. Zbl 1307.35030
Krehel, Oleh; Aiki, Toyohiko; Muntean, Adrian
2014
Behavior of free boundaries of blow-up solutions to one-phase Stefan problems. Zbl 0859.35141
Aiki, Toyohiko
1996
Multi-dimensional Stefan problems with dynamic boundary conditions. Zbl 0833.35153
Aiki, Toyohiko
1995
Existence and uniqueness of solutions to a mathematical model predicting service life of concrete structures. Zbl 1181.35344
2009
A mathematical model for bacterial growth described by a hysteresis operator. Zbl 1343.35131
Aiki, Toyohiko; Kopfová, Jana
2008
One-dimensional shape memory alloy problems including a hysteresis operator. Zbl 1305.74070
Aiki, Toyohiko
2003
Uniqueness of solutions to a mathematical model describing moisture transport in concrete materials. Zbl 1302.74073
Aiki, Toyohiko; Kumazaki, Kota
2014
A one dimensional free boundary problem for adsorption phenomena. Zbl 1310.35246
Sato, Naoki; Aiki, Toyohiko; Murase, Yusuke; Shirakawa, Ken
2014
Large-time asymptotics of moving-reaction interfaces involving nonlinear Henry’s law and time-dependent Dirichlet data. Zbl 1282.35418
2013
A model of 3D shape memory alloy materials. Zbl 1076.74041
Aiki, Toyohiko
2005
Well-posedness of one-phase Stefan problems for sublinear heat equations. Zbl 1010.35118
Aiki, Toyohiko; Imai, Hitoshi; Ishimura, Naoyuki; Yamada, Yoshio
2002
Global existence of solutions to one-phase Stefan problems for semilinear parabolic equations. Zbl 0954.35154
Aiki, Toyohiko; Imai, Hitoshi
1998
Periodic stability of solutions to some degenerate parabolic equations with dynamic boundary conditions. Zbl 0846.35013
Aiki, Toyohiko
1996
Two-phase Stefan problems with dynamic boundary conditions. Zbl 0783.35083
Aiki, Toyohiko
1993
Behavior of solutions to two-phase Stefan problems for nonlinear parabolic equations. Zbl 0761.35112
1991
Distributed space scales in a semilinear reaction-diffusion system including a parabolic variational inequality: A well-posedness study. Zbl 1427.35119
Fatima, Tasnim; Muntean, Adrian; Aiki, Toyohiko
2012
On uniqueness of a weak solution of one-dimensional concrete carbonation problem. Zbl 1210.35296
2011
Phase field equations with constraints under nonlinear dynamic boundary conditions. Zbl 1084.35521
Sato, Naoki; Aiki, Toyohiko
2001
Some models for shape memory alloys. Zbl 1036.74042
2001
Blow-up points to one phase Stefan problems with Dirichlet boundary conditions. Zbl 0881.35128
Aiki, Toyohiko
1996
Behaviour of blow-up solutions to one-phase Stefan problems with Dirichlet boundary conditions. Zbl 0864.35122
Aiki, T.; Imai, H.
1996
Multi-dimensional two-phase Stefan problems with nonlinear dynamic boundary conditions. Zbl 0868.35061
Aiki, Toyohiko
1995
The existence of solutions of two-phase Stefan problems for nonlinear parabolic equations. Zbl 0754.35189
Aiki, Toyohiko
1990
Multiscale model for moisture transport with adsorption phenomenon in concrete materials. Zbl 1390.35430
Kumazaki, Kota; Aiki, Toyohiko; Sato, Naoki; Murase, Yusuke
2018
Relaxation for a control problem in concrete carbonation modeling. Zbl 1378.49005
Aiki, Toyohiko; Timoshin, Sergey A.
2017
Existence and uniqueness for a concrete carbonation process with hysteresis. Zbl 1366.35069
Aiki, Toyohiko; Timoshin, Sergey A.
2017
On a large time behavior of a solution to a one-dimensional free boundary problem for adsorption phenomena. Zbl 1386.35484
Aiki, Toyohiko; Murase, Yusuke
2017
Weak solutions for Falk’s model of shape memory alloys. Zbl 0989.74053
Aiki, Toyohiko
2000
Periodic stability for some degenerate parabolic equations with nonlinear flux conditions. Zbl 0762.35051
Aiki, Toyohiko; Shinoda, Junichi; Kenmochi, Nobuyuki
1991
Control of biological models with hysteresis. Zbl 1425.92164
Timoshin, Sergey A.; Aiki, Toyohiko
2019
Large-time behavior of solutions to a thermo-diffusion system with Smoluchowski interactions. Zbl 1378.35303
2017
On a one-dimensional shape-memory alloy model in its fast-temperature-activation limit. Zbl 1243.74017
Aiki, Toyohiko; Anthonissen, Martijn; Muntean, Adrian
2012
One-dimensional shape memory alloy problem with Duhem type of hysteresis operator. Zbl 1111.74033
Aiki, Toyohiko; Okazaki, Takanobu
2007
Mathematical models for phase change problems with hysteresis effect. Zbl 1224.35440
Aiki, T.; Minchev, E.; Okazaki, T.
2005
One-phase Stefan problems for sublinear heat equations: asymptotic behavior of solutions. Zbl 1091.35117
Aiki, Toyohiko; Imai, Hitoshi; Ishimura, Naoyuki; Yamada, Yoshio
2004
Models for shape memory alloys described by subdifferentials of indicator functions. Zbl 1028.35172
2002
Phase field equations with constraints under nonlinear dynamic boundary conditions. Zbl 1374.35215
Sato, Naoki; Aiki, Toyohiko
2001
Optimal control problem for phase-field equations with nonlinear dynamic boundary conditions. Zbl 1042.49530
Aiki, Toyohiko; Kadoya, Atsushi; Sato, Naoki
2001
Stefan problems in several space variables with dynamic boundary conditions. Zbl 0846.35149
Aiki, Toyohiko
1996
Periodic stability of solutions to two-phase Stefan problems with nonlinear boundary condition. Zbl 0813.35138
Aiki, Toyohiko
1994
Two-phase Stefan problems for parabolic-elliptic equations. Zbl 0701.35158
Aiki, Toyohiko
1988
Control of biological models with hysteresis. Zbl 1425.92164
Timoshin, Sergey A.; Aiki, Toyohiko
2019
Multiscale model for moisture transport with adsorption phenomenon in concrete materials. Zbl 1390.35430
Kumazaki, Kota; Aiki, Toyohiko; Sato, Naoki; Murase, Yusuke
2018
Relaxation for a control problem in concrete carbonation modeling. Zbl 1378.49005
Aiki, Toyohiko; Timoshin, Sergey A.
2017
Existence and uniqueness for a concrete carbonation process with hysteresis. Zbl 1366.35069
Aiki, Toyohiko; Timoshin, Sergey A.
2017
On a large time behavior of a solution to a one-dimensional free boundary problem for adsorption phenomena. Zbl 1386.35484
Aiki, Toyohiko; Murase, Yusuke
2017
Large-time behavior of solutions to a thermo-diffusion system with Smoluchowski interactions. Zbl 1378.35303
2017
Homogenization of a thermo-diffusion system with Smoluchowski interactions. Zbl 1307.35030
Krehel, Oleh; Aiki, Toyohiko; Muntean, Adrian
2014
Uniqueness of solutions to a mathematical model describing moisture transport in concrete materials. Zbl 1302.74073
Aiki, Toyohiko; Kumazaki, Kota
2014
A one dimensional free boundary problem for adsorption phenomena. Zbl 1310.35246
Sato, Naoki; Aiki, Toyohiko; Murase, Yusuke; Shirakawa, Ken
2014
A free-boundary problem for concrete carbonation: front nucleation and rigorous justification of the $$\sqrt{{t}}$$-law of propagation. Zbl 1276.35127
2013
Large-time asymptotics of moving-reaction interfaces involving nonlinear Henry’s law and time-dependent Dirichlet data. Zbl 1282.35418
2013
Distributed space scales in a semilinear reaction-diffusion system including a parabolic variational inequality: A well-posedness study. Zbl 1427.35119
Fatima, Tasnim; Muntean, Adrian; Aiki, Toyohiko
2012
On a one-dimensional shape-memory alloy model in its fast-temperature-activation limit. Zbl 1243.74017
Aiki, Toyohiko; Anthonissen, Martijn; Muntean, Adrian
2012
Well-posedness of a mathematical model for moisture transport appearing in concrete carbonation process. Zbl 1282.35186
Aiki, Toyohiko; Kumazaki, Kota
2011
On uniqueness of a weak solution of one-dimensional concrete carbonation problem. Zbl 1210.35296
2011
Large time behavior of solutions to a moving-interface problem modeling concrete carbonation. Zbl 1202.35362
2010
Existence and uniqueness of solutions to a mathematical model predicting service life of concrete structures. Zbl 1181.35344
2009
A mathematical model for bacterial growth described by a hysteresis operator. Zbl 1343.35131
Aiki, Toyohiko; Kopfová, Jana
2008
One-dimensional shape memory alloy problem with Duhem type of hysteresis operator. Zbl 1111.74033
Aiki, Toyohiko; Okazaki, Takanobu
2007
A prey-predator model with hysteresis effect. Zbl 1086.35154
Aiki, Toyohiko; Minchev, Emil
2005
A model of 3D shape memory alloy materials. Zbl 1076.74041
Aiki, Toyohiko
2005
Mathematical models for phase change problems with hysteresis effect. Zbl 1224.35440
Aiki, T.; Minchev, E.; Okazaki, T.
2005
One-phase Stefan problems for sublinear heat equations: asymptotic behavior of solutions. Zbl 1091.35117
Aiki, Toyohiko; Imai, Hitoshi; Ishimura, Naoyuki; Yamada, Yoshio
2004
One-dimensional shape memory alloy problems including a hysteresis operator. Zbl 1305.74070
Aiki, Toyohiko
2003
Well-posedness of one-phase Stefan problems for sublinear heat equations. Zbl 1010.35118
Aiki, Toyohiko; Imai, Hitoshi; Ishimura, Naoyuki; Yamada, Yoshio
2002
Models for shape memory alloys described by subdifferentials of indicator functions. Zbl 1028.35172
2002
Phase field equations with constraints under nonlinear dynamic boundary conditions. Zbl 1084.35521
Sato, Naoki; Aiki, Toyohiko
2001
Some models for shape memory alloys. Zbl 1036.74042
2001
Phase field equations with constraints under nonlinear dynamic boundary conditions. Zbl 1374.35215
Sato, Naoki; Aiki, Toyohiko
2001
Optimal control problem for phase-field equations with nonlinear dynamic boundary conditions. Zbl 1042.49530
Aiki, Toyohiko; Kadoya, Atsushi; Sato, Naoki
2001
Weak solutions for Falk’s model of shape memory alloys. Zbl 0989.74053
Aiki, Toyohiko
2000
Global existence of solutions to one-phase Stefan problems for semilinear parabolic equations. Zbl 0954.35154
Aiki, Toyohiko; Imai, Hitoshi
1998
Behavior of free boundaries of blow-up solutions to one-phase Stefan problems. Zbl 0859.35141
Aiki, Toyohiko
1996
Periodic stability of solutions to some degenerate parabolic equations with dynamic boundary conditions. Zbl 0846.35013
Aiki, Toyohiko
1996
Blow-up points to one phase Stefan problems with Dirichlet boundary conditions. Zbl 0881.35128
Aiki, Toyohiko
1996
Behaviour of blow-up solutions to one-phase Stefan problems with Dirichlet boundary conditions. Zbl 0864.35122
Aiki, T.; Imai, H.
1996
Stefan problems in several space variables with dynamic boundary conditions. Zbl 0846.35149
Aiki, Toyohiko
1996
Multi-dimensional Stefan problems with dynamic boundary conditions. Zbl 0833.35153
Aiki, Toyohiko
1995
Multi-dimensional two-phase Stefan problems with nonlinear dynamic boundary conditions. Zbl 0868.35061
Aiki, Toyohiko
1995
Periodic stability of solutions to two-phase Stefan problems with nonlinear boundary condition. Zbl 0813.35138
Aiki, Toyohiko
1994
Two-phase Stefan problems with dynamic boundary conditions. Zbl 0783.35083
Aiki, Toyohiko
1993
Behavior of solutions to two-phase Stefan problems for nonlinear parabolic equations. Zbl 0761.35112
1991
Periodic stability for some degenerate parabolic equations with nonlinear flux conditions. Zbl 0762.35051
Aiki, Toyohiko; Shinoda, Junichi; Kenmochi, Nobuyuki
1991
The existence of solutions of two-phase Stefan problems for nonlinear parabolic equations. Zbl 0754.35189
Aiki, Toyohiko
1990
Two-phase Stefan problems for parabolic-elliptic equations. Zbl 0701.35158
Aiki, Toyohiko
1988
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#### Cited by 111 Authors

 20 Aiki, Toyohiko 8 Muntean, Adrian 6 Fukao, Takeshi 6 Timoshin, Sergey A. 5 Kumazaki, Kota 4 Colli, Pierluigi 4 Imai, Hitoshi 4 Minchev, Emil 4 Stefanelli, Ulisse 3 Chainais-Hillairet, Claire 3 Gal, Ciprian Gheorghe Sorin 3 Krejčí, Pavel 3 Murase, Yusuke 3 Nikolopoulos, Christos V. 3 Sato, Naoki 3 Shirakawa, Ken 3 Wang, Yifu 3 Zheng, Jiashan 2 Beneš, Michal 2 Grasselli, Maurizio 2 Igbida, Noureddine 2 Ishimura, Naoyuki 2 Kajikiya, Ryuji 2 Khoa, Vo Anh 2 Miranville, Alain M. 2 Roubíček, Tomáš 1 Akagi, Goro 1 Alqahtani, Awatif 1 Ambrosio, Vincenzo 1 Andreu, Fuensanta 1 Bataillon, Christian 1 Böhm, Michael C. 1 Bouchon, François 1 Cavaterra, Cecilia 1 Chen, Xiaoshan 1 Chen, Yingshan 1 Cirillo, Emilio Nicola Maria 1 Colangeli, Matteo 1 Company, Rafael 1 Darbenas, Zymantas 1 Desvillettes, Laurent 1 Eleuteri, Michela 1 Fuhrmann, Jürgen 1 Gallouët, Thomas O. 1 Gavrilov, Vladimir S. 1 Ghidouche, Hamid 1 Giga, Yoshikazu 1 Grandi, Diego 1 Gurevich, Pavel L. 1 Hassan Farshbaf-Shaker, M. 1 Hoarau, E. 1 Ijioma, Ekeoma Rowland 1 Jiménez-Casas, Angela 1 Jleli, Mohamed 1 Jódar Sanchez, Lucas Antonio 1 Jüngel, Ansgar 1 Ke, Yuanyuan 1 Kenmochi, Nobuyuki 1 Kikuchi, Koji 1 Kirane, Mokhtar 1 Kopfová, Jana 1 Krupička, Lukáš 1 Li, Huiling 1 Lin, Zhigui 1 Ling, Zhi 1 Lorenzani, Silvia 1 Lu, Xueyan 1 Lussardi, Luca 1 Mazón Ruiz, José M. 1 Merlet, Benoît 1 Motoda, Taishi 1 Nakane, Kazuaki 1 Nakayashiki, Ryota 1 Okazaki, Takanobu 1 Oliver, Marcel 1 Omata, Seiro 1 Ôtani, Mitsuharu 1 Pažanin, Igor 1 Piqueras, Miguel A. 1 Ptashnyk, Mariya 1 Reichelt, Sina 1 Rodríguez-Bernal, Aníbal 1 Rybka, Piotr 1 Sacks, Paul E. 1 Samet, Bessem 1 Soltanov, Kamal N. 1 Souplet, Philippe 1 Sun, Ningkui 1 Suzuki, Takashi 1 Tachikawa, Tomomi 1 Tang, Qiulin 1 Tarzia, Domingo Alberto 1 Tasaki, Souhei 1 Thieu, Thi Kim Thoa 1 Tikhomirov, Sergey B. 1 Toledo, J. Julián 1 Tolstonogov, Aleksandr Aleksandrovich 1 Tomassetti, Giuseppe 1 Touzani, Rachid 1 Vermolen, Fred J. ...and 11 more Authors
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#### Cited in 44 Serials

 11 Journal of Mathematical Analysis and Applications 9 Nonlinear Analysis. Theory, Methods & Applications. Series A: Theory and Methods 7 Journal of Differential Equations 5 Nonlinear Analysis. Real World Applications 3 Mathematical Methods in the Applied Sciences 3 Networks and Heterogeneous Media 3 Discrete and Continuous Dynamical Systems. Series S 2 ZAMP. Zeitschrift für angewandte Mathematik und Physik 2 Journal of Computational and Applied Mathematics 2 SIAM Journal on Control and Optimization 2 Continuum Mechanics and Thermodynamics 2 Discrete and Continuous Dynamical Systems. Series B 2 Communications on Pure and Applied Analysis 2 Multiscale Modeling & Simulation 2 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 2 Izvestiya Irkutskogo Gosudarstvennogo Universiteta. Seriya Matematika 2 Nonlinear Analysis. Theory, Methods & Applications 1 Applicable Analysis 1 Computers & Mathematics with Applications 1 Journal of Computational Physics 1 Journal of Engineering Mathematics 1 Rocky Mountain Journal of Mathematics 1 Annali di Matematica Pura ed Applicata. Serie Quarta 1 Czechoslovak Mathematical Journal 1 Numerical Functional Analysis and Optimization 1 Proceedings of the American Mathematical Society 1 Quarterly of Applied Mathematics 1 Systems & Control Letters 1 Acta Applicandae Mathematicae 1 Annales de l’Institut Henri Poincaré. Analyse Non Linéaire 1 Asymptotic Analysis 1 Japan Journal of Industrial and Applied Mathematics 1 SIAM Journal on Applied Mathematics 1 Journal of Nonlinear Science 1 Applied Mathematics. Series B (English Edition) 1 NoDEA. Nonlinear Differential Equations and Applications 1 Sbornik: Mathematics 1 Discrete and Continuous Dynamical Systems 1 Mathematics and Mechanics of Solids 1 Communications in Contemporary Mathematics 1 Bulletin of the Malaysian Mathematical Sciences Society. Second Series 1 Asia-Pacific Financial Markets 1 Evolution Equations and Control Theory 1 Journal of Elliptic and Parabolic Equations
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#### Cited in 17 Fields

 78 Partial differential equations (35-XX) 17 Mechanics of deformable solids (74-XX) 16 Classical thermodynamics, heat transfer (80-XX) 9 Calculus of variations and optimal control; optimization (49-XX) 8 Biology and other natural sciences (92-XX) 7 Ordinary differential equations (34-XX) 7 Operator theory (47-XX) 7 Fluid mechanics (76-XX) 5 Numerical analysis (65-XX) 4 Statistical mechanics, structure of matter (82-XX) 3 Systems theory; control (93-XX) 2 Dynamical systems and ergodic theory (37-XX) 2 Optics, electromagnetic theory (78-XX) 2 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Difference and functional equations (39-XX) 1 Integral equations (45-XX) 1 Operations research, mathematical programming (90-XX)