Faculty Profiles - KUBO Masahiro

写真a

KUBO Masahiro

Name of department

Faculty of Systems Engineering, Fundamental Subjects

Job title

Professor

Mail Address

Homepage

External link

Education

1985

-

1988

東京大学大学院理学系研究科博士課程相関理化学専攻
1983

-

1985

千葉大学大学院理学研究科修士課程数学専攻
1980

-

1983

The University of Tokyo College of Arts and Sciences Department of Basic Science
1978

-

1980

The University of Tokyo 理科Ⅱ類

Degree

(BLANK)

Academic & Professional Experience

2015.04

-

Now

Wakayama University Faculty of Systems Engineering 教授
2006.04

-

2015.03

Nagoya Institute of Technology Graduate School of Engineering Professor
1990.04

-

2006.03

Saga University Faculty of Science and Engineering 助教授
1988.04

-

1990.03

Saga University Faculty of Science and Engineering 助手

Research Areas

Natural sciences / Mathematical analysis

Classes (including Experimental Classes, Seminars, Graduation Thesis Guidance, Graduation Research, and Topical Research)

2023 Applied Analysis Specialized Subjects
2023 Linear Algebra 2 Specialized Subjects
2023 Linear Algebra 1 Specialized Subjects
2023 Linear Algebra 1 Specialized Subjects
2023 Linear Algebra 1 Specialized Subjects
2023 Linear Algebra 2 Specialized Subjects
2023 Linear Algebra 2 Specialized Subjects
2022 Linear Algebra 2 Specialized Subjects
2022 Linear Algebra 2 Specialized Subjects
2022 Linear Algebra 2 Specialized Subjects
2022 Linear Algebra 1 Specialized Subjects
2022 Linear Algebra 1 Specialized Subjects
2022 Linear Algebra 1 Specialized Subjects
2022 Linear Algebra 1 Specialized Subjects
2022 Applied Analysis Specialized Subjects
2022 Introductory Seminar in Systems Engineering Specialized Subjects
2021 Linear Algebra 2 Specialized Subjects
2021 Linear Algebra 2 Specialized Subjects
2021 Linear Algebra 2 Specialized Subjects
2021 Linear Algebra 2 Specialized Subjects
2021 Linear Algebra 1 Specialized Subjects
2021 Linear Algebra 1 Specialized Subjects
2021 Linear Algebra 1 Specialized Subjects
2021 Linear Algebra 1 Specialized Subjects
2021 Linear Algebra 1 Specialized Subjects
2021 Applied Analysis Specialized Subjects
2020 Introductory Seminar in Systems Engineering Specialized Subjects
2020 Linear Algebra 2 Specialized Subjects
2020 Linear Algebra 2 Specialized Subjects
2020 Linear Algebra 1 Specialized Subjects
2020 Applied Analysis Specialized Subjects
2019 Linear Algebra 2 Specialized Subjects
2019 Linear Algebra 2 Specialized Subjects
2019 Linear Algebra 1 Specialized Subjects
2019 Applied Analysis Specialized Subjects
2018 Linear Algebra 2 Specialized Subjects
2018 Linear Algebra 1 Specialized Subjects
2018 Applied Analysis Specialized Subjects
2017 Introductory Seminar in Systems Engineering Specialized Subjects
2017 Linear Algebra 2 Specialized Subjects
2017 Linear Algebra 2 Specialized Subjects
2017 Linear Algebra 1 Specialized Subjects
2017 Applied Analysis Specialized Subjects
2016 Linear Algebra 2 Specialized Subjects
2016 Linear Algebra 2 Specialized Subjects
2016 Linear Algebra 1 Specialized Subjects
2016 Applied Analysis Specialized Subjects
2015 Linear Algebra 1 Specialized Subjects
2015 Applied Analysis Specialized Subjects
2015 Linear Algebra 2 Specialized Subjects

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Classes

2023 Systems Engineering Project SeminarⅡB Master's Course
2023 Systems Engineering Project SeminarⅡA Master's Course
2023 Systems Engineering Project SeminarⅠB Master's Course
2023 Systems Engineering Project SeminarⅠA Master's Course
2023 Systems Engineering SeminarⅡB Master's Course
2023 Systems Engineering SeminarⅡA Master's Course
2023 Systems Engineering SeminarⅠB Master's Course
2023 Systems Engineering SeminarⅠA Master's Course
2023 Systems Engineering Advanced Seminar Ⅰ Doctoral Course
2023 Systems Engineering Advanced Seminar Ⅰ Doctoral Course
2023 Systems Engineering Advanced Seminar Ⅱ Doctoral Course
2023 Systems Engineering Advanced Seminar Ⅱ Doctoral Course
2023 Systems Engineering Advanced Research Doctoral Course
2023 Systems Engineering Advanced Research Doctoral Course
2023 Systems Engineering Global Seminar Ⅰ Doctoral Course
2023 Systems Engineering Global Seminar Ⅰ Doctoral Course
2023 Systems Engineering Global Seminar Ⅱ Doctoral Course
2023 Systems Engineering Global Seminar Ⅱ Doctoral Course
2022 Systems Engineering Global Seminar Ⅱ Doctoral Course
2022 Systems Engineering Global Seminar Ⅰ Doctoral Course
2022 Systems Engineering Advanced Research Doctoral Course
2022 Systems Engineering Advanced Seminar Ⅱ Doctoral Course
2022 Systems Engineering Advanced Seminar Ⅰ Doctoral Course
2022 Systems Engineering Project SeminarⅡB Master's Course
2022 Systems Engineering Project SeminarⅡA Master's Course
2022 Systems Engineering Project SeminarⅠB Master's Course
2022 Systems Engineering Project SeminarⅠA Master's Course
2022 Systems Engineering SeminarⅡB Master's Course
2022 Systems Engineering SeminarⅡA Master's Course
2022 Systems Engineering SeminarⅠB Master's Course
2022 Systems Engineering SeminarⅠA Master's Course
2021 Systems Engineering Global Seminar Ⅱ Doctoral Course
2021 Systems Engineering Global Seminar Ⅰ Doctoral Course
2021 Systems Engineering Advanced Research Doctoral Course
2021 Systems Engineering Advanced Seminar Ⅱ Doctoral Course
2021 Systems Engineering Advanced Seminar Ⅰ Doctoral Course
2021 Systems Engineering Project SeminarⅡB Master's Course
2021 Systems Engineering Project SeminarⅡA Master's Course
2021 Systems Engineering Project SeminarⅠB Master's Course
2021 Systems Engineering Project SeminarⅠA Master's Course
2021 Systems Engineering SeminarⅡB Master's Course
2021 Systems Engineering SeminarⅡA Master's Course
2021 Systems Engineering SeminarⅠB Master's Course
2021 Systems Engineering SeminarⅠA Master's Course
2020 Systems Engineering Global Seminar Ⅱ Doctoral Course
2020 Systems Engineering Global Seminar Ⅰ Doctoral Course
2020 Systems Engineering Advanced Research Doctoral Course
2020 Systems Engineering Advanced Seminar Ⅱ Doctoral Course
2020 Systems Engineering Advanced Seminar Ⅰ Doctoral Course
2020 Systems Engineering Project SeminarⅡB Master's Course
2020 Systems Engineering Project SeminarⅡA Master's Course
2020 Systems Engineering Project SeminarⅠB Master's Course
2020 Systems Engineering Project SeminarⅠA Master's Course
2020 Systems Engineering SeminarⅡB Master's Course
2020 Systems Engineering SeminarⅡA Master's Course
2020 Systems Engineering SeminarⅠB Master's Course
2020 Systems Engineering SeminarⅠA Master's Course
2019 Systems Engineering Advanced Research Doctoral Course
2019 Systems Engineering Advanced Research Doctoral Course
2019 Systems Engineering SeminarⅡB Master's Course
2019 Systems Engineering SeminarⅡA Master's Course
2019 Systems Engineering SeminarⅠB Master's Course
2019 Systems Engineering SeminarⅠA Master's Course
2019 Systems Engineering Global Seminar Ⅰ Doctoral Course
2019 Systems Engineering Global Seminar Ⅰ Doctoral Course
2019 Systems Engineering Project SeminarⅡB Master's Course
2019 Systems Engineering Project SeminarⅡA Master's Course
2019 Systems Engineering Project SeminarⅡA Master's Course
2019 Systems Engineering Project SeminarⅠB Master's Course
2019 Systems Engineering Project SeminarⅠA Master's Course
2018 Systems Engineering Global Seminar Ⅱ Doctoral Course
2018 Systems Engineering Global Seminar Ⅱ Doctoral Course
2018 Systems Engineering Advanced Research Doctoral Course
2018 Systems Engineering Advanced Research Doctoral Course
2018 Systems Engineering Project SeminarⅡB Master's Course
2018 Systems Engineering Project SeminarⅡA Master's Course
2018 Systems Engineering Project SeminarⅠB Master's Course
2018 Systems Engineering Project SeminarⅠA Master's Course
2018 Systems Engineering SeminarⅡB Master's Course
2018 Systems Engineering SeminarⅡA Master's Course
2018 Systems Engineering SeminarⅠB Master's Course
2018 Systems Engineering SeminarⅠA Master's Course
2017 Systems Engineering Global Seminar Ⅰ Doctoral Course
2017 Systems Engineering Advanced Research Doctoral Course
2017 Systems Engineering Advanced Seminar Ⅱ Doctoral Course
2017 Systems Engineering Project SeminarⅡA Master's Course
2017 Systems Engineering Project SeminarⅠA Master's Course
2017 Systems Engineering SeminarⅡB Master's Course
2017 Systems Engineering SeminarⅡA Master's Course
2017 Systems Engineering SeminarⅠB Master's Course
2017 Systems Engineering SeminarⅠA Master's Course
2016 Systems Engineering Global Seminar Ⅱ Doctoral Course
2016 Systems Engineering Global Seminar Ⅱ Doctoral Course
2016 Systems Engineering Advanced Research Doctoral Course
2016 Systems Engineering Advanced Research Doctoral Course
2016 Systems Engineering Advanced Seminar Ⅱ Doctoral Course
2016 Systems Engineering Advanced Seminar Ⅱ Doctoral Course
2016 Systems Engineering Project SeminarⅡB Master's Course
2016 Systems Engineering Project SeminarⅡA Master's Course
2016 Systems Engineering Project SeminarⅠB Master's Course
2016 Systems Engineering Project SeminarⅠA Master's Course
2016 Systems Engineering SeminarⅡB Master's Course
2016 Systems Engineering SeminarⅡA Master's Course
2016 Systems Engineering SeminarⅠB Master's Course
2016 Systems Engineering SeminarⅠA Master's Course
2016 Information and Communications Technology for Civilized Society Master's Course
2015 Systems Engineering Advanced Seminar Ⅱ
2015 Systems Engineering Advanced Seminar Ⅰ
2015 Systems Engineering Advanced Research
2015 Systems Engineering SeminarⅡA
2015 Systems Engineering SeminarⅠA
2015 Systems Engineering Project SeminarⅡA
2015 Systems Engineering Project SeminarⅠA
2015 Systems Engineering Global Seminar Ⅰ
2015 Systems Engineering Advanced Seminar Ⅱ
2015 Systems Engineering Advanced Seminar Ⅰ
2015 Systems Engineering Advanced Research
2015 Systems Engineering SeminarⅡB
2015 Systems Engineering SeminarⅠB
2015 Systems Engineering Project SeminarⅡB
2015 Systems Engineering Project SeminarⅠB
2015 Systems Engineering Global Seminar Ⅰ

▼display all

Satellite Courses

2016 Information and Communications Technology for Civilized Society

Research Interests

nonlinear analysis
非線形解析

Published Papers

Elliptic-Parabolic Quasi-Variational Evolution Equations

Masahiro Kubo, Noriaki Yamazaki

FUNKCIALAJ EKVACIOJ 67 ( 1 ) 1 - 27 2024.04 [Refereed]
Periodic solutions to a class of quasi-variational evolution equations

Masahiro Kubo, Noriaki Yamazaki

Journal of Differential Equations 384 165 - 192 2024.03 [Refereed]
Time-dependent subdifferential evolution equations and quasi-variational evolution equations

Masahiro Kubo

2 0 2 2 年度日本数学会年会総合講演・企画特別講演アブストラクト 51 - 66 2022.03 [Invited]
Global strong solutions to abstract quasi-variational evolution equations

Masahiro Kubo, Noriaki Yamazaki

Journal of Differential Equations ( Academic Press Inc. ) 265 ( 9 ) 4158 - 4180 2018 [Refereed]

　View Summary

We prove the existence of a time-global strong solution of a class of abstract quasi-variational evolution equations and apply the abstract result to concrete parabolic variational and quasi-variational inequalities.

DOI
Quasi-variational analysis

Masahiro Kubo

Sugaku Expositions 30 ( 1 ) 17 - 34 2017.06 [Refereed] [Invited]
Quasi-subdifferential operator approach to elliptic variational and quasi-variational inequalities

M. Kubo, Y. Murase

MATHEMATICAL METHODS IN THE APPLIED SCIENCES ( WILEY-BLACKWELL ) 39 ( 18 ) 5626 - 5635 2016.12 [Refereed]

　View Summary

We prove an existence theorem for an abstract operator equation associated with a quasi-subdifferential operator and then apply it to concrete elliptic variational and quasi-variational inequalities. Copyright (c) 2016 John Wiley & Sons, Ltd.

DOI
Quasi-variational principles and quasi-subdifferential operators

Msashiro Kubo

GAKUTO International Series. Mathematical Sciences and Applications 36 165 - 174 2013.11 [Refereed]
Quasi-subdifferential operators and evolution equations

M. Kubo

Discrete and Continuous Dynamical Systems supplement 447 - 456 2013.11 [Refereed]
準変分解析

久保雅弘

数学 65 ( 4 ) 385 - 401 2013.10 [Refereed] [Invited]
Quasi-Subdifferential Operators and Quasi-Subdifferential Evolution Equations (New developments of the theory of evolution equations in the analysis of non-equilibria)

Kubo Masahiro

RIMS Kokyuroku ( Kyoto University ) 1856 24 - 33 2013.10 [Invited]
The Cahn-Hilliard equation with time-dependent constraint

Masahiro Kubo

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS ( PERGAMON-ELSEVIER SCIENCE LTD ) 75 ( 14 ) 5672 - 5685 2012.09 [Refereed]

　View Summary

We propose an abstract variational inequality formulation of the Cahn-Hilliard equation with a time-dependent constraint. We introduce notions of strong and weak solutions, and prove that a strong solution, if it exists, is a weak solution, and that the existence of a unique weak solution holds under an appropriate time-dependence condition on the constraint. We also show that the weak solution is a strong solution under appropriate assumptions on the data. Our abstract results can be applied to various concrete problems. (C) 2012 Elsevier Ltd. All rights reserved.

DOI
Variational inequalities for a system of elliptic-parabolic equations

M. Kubo, K. Shirakawa, N. Yamazaki

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS ( ACADEMIC PRESS INC ELSEVIER SCIENCE ) 387 ( 2 ) 490 - 511 2012.03 [Refereed]

　View Summary

We create a general framework for mathematical study of variational inequalities for a system of elliptic-parabolic equations. In this paper, we establish a solvability theorem concerning the existence of solutions for the vector-valued elliptic-parabolic variational inequality with time-dependent constraint. Moreover, we give some applications of the system, for example, time-dependent boundary obstacle problem and time-dependent interior obstacle problem. (C) 2011 Elsevier Inc. All rights reserved.

DOI
Variational inequalities for a non-isothermal phase field model

Kota Kumazaki, Masahiro Kubo

Discrete and Continuous Dynamical Systems - Series S 4 ( 2 ) 409 - 421 2011.04 [Refereed]

　View Summary

We study variational inequalities for a non-isothermal phase field model of the Penrose-Fife type. We consider time-dependent constraints for the order parameter and the Dirichlet boundary condition for the temperature.

DOI
Variational inequalities with time-dependent constraints in L-p

Masahiro Kubo

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS ( PERGAMON-ELSEVIER SCIENCE LTD ) 73 ( 2 ) 390 - 398 2010.07 [Refereed]

　View Summary

We propose an abstract variational inequality with time-dependent constraints in a Banach space with a uniformly convex dual and establish the existence, uniqueness, and regularity of the solution thereof. The abstract result is applied to concrete variational inequalities with time-dependent constraints, thereby obtaining the L-p-regularity of solutions. (C) 2010 Elsevier Ltd. All rights reserved.

DOI
A system of evolution equations for non-isothermal phase transitions

Masahiro Kubo, Kota Kumazaki

JOURNAL OF EVOLUTION EQUATIONS ( BIRKHAUSER VERLAG AG ) 10 ( 1 ) 129 - 145 2010.03 [Refereed]

　View Summary

We propose and study a system of evolution equations. This is an abstract formulation of problems arising in non-isothermal phase transitions. We consider time-dependent constraints on the unknown functions. Thus the problem yields a system of parabolic variational inequalities. We prove the existence of a solution in a general framework, and then apply the abstract result to some models of phase transitions.

DOI
Global attractor of double obstacle problem in thermohydraulics

Takeshi Fukao, Masahiro Kubo

GAKUTO International Series. Mathematical Sciences and Applications 32 273 - 287 2010.02 [Refereed]
A non-isothermal phase separation with constraints and Dirichlet boundary condition for temperature

Kota Kumazaki, Akio Ito, Masahiro Kubo

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS ( PERGAMON-ELSEVIER SCIENCE LTD ) 71 ( 5-6 ) 1950 - 1963 2009.09 [Refereed]

　View Summary

We consider non-isothermal phase separation models of the Penrose-Fife type, which were proposed in [O. Penrose, P.C. Fife, Thermodynamically consistent models of phase-field type for the kinetics of phase transitions, Physica D 43 (1990) 44-62]. In the present paper, we impose a non-homogeneous Dirichlet boundary condition on the nonlinear heat flux. Moreover, we consider two cases as boundary conditions for the conserved order parameter. One is the homogeneous Neumann boundary condition and the other is the Signorini boundary condition, which is nonlinear.
We show the existence and uniqueness of solutions to these models. (C) 2009 Elsevier Ltd. All rights reserved.

DOI
Generalized solutions of a non-isothermal phase separation model

K. Kumazaki, A. Ito, M. Kubo

Discrete and Continuous Dynamical Systems supplement 2009 476 - 485 2009.09 [Refereed]
Time-dependent obstacle problem in thermohydraulics

T. Fukao, M. Kubo

Discrete and Continuous Dynamical Systems supplement 2009 240 - 249 2009.09 [Refereed]
Singular perturbations for variational inequalities with time-dependent constraints

Masahiro Kubo

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS ( ACADEMIC PRESS INC ELSEVIER SCIENCE ) 356 ( 1 ) 60 - 68 2009.08 [Refereed]

　View Summary

We study an abstract hyperbolic variational inequality with a (small) parameter and with time-dependent subdifferentials in a real Hilbert space. We prove that its Solution converges to a solution of a parabolic variational inequality as the parameter tends to zero. We also explain how to apply the abstract theory to concrete unilateral problems. (C) 2009 Elsevier Inc. All rights reserved.

DOI
Convergence and optimal control problems for elliptic-parabolic variational inequalities with time-dependent constraints

M. Kubo, N. Yamazaki

Advances in Mathematical Sciences and Applications 19 ( 1 ) 155 - 183 2009.07 [Refereed]
Time-dependent double obstacle problem in thermohydraulics

Takeshi Fukao, Masahiro Kubo

GAKUTO International Series. Mathematical Sciences and Applications 29 73 - 92 2008.08 [Refereed]
Well-posedness for an extended Penrose-Fife phase-field model with energy balance supplied by Dirichlet boundary conditions

Akio Ito, Masahiro Kubo

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS ( PERGAMON-ELSEVIER SCIENCE LTD ) 9 ( 2 ) 370 - 383 2008.04 [Refereed]

　View Summary

In this study we consider the non-isothermal phase-field model proposed by Penrose and Fife [Thermodynamically consistent models of phase-field type for the kinetics of phase transitions, Physica D 43 (1990) 44-62]. The system consists of the energy balance law (a nonlinear heat equation) and an equation that describes space-time changes in the order parameter (the Ginzburg-Landau equation). For the energy balance law, we consider the general nonlinear heat flux arising in non-equilibrium thermodynamics and impose the Dirichlet boundary condition. For the order parameter, we impose a constraint and thus consider a parabolic variational inequality. We prove the well-posedness of the problem: the system yields a unique solution that depends continuously upon given data. (c) 2007 Elsevier Ltd. All rights reserved.

DOI
Well-posedness and periodic stability for quasilinear parabolic variational inequalities with time-dependent constraints

Ken Shirakawa, Masahiro Kubo, Noriaki Yamazaki

Recent Advances in Nonlinear Analysis, World Scientific ( World Scientific Publishing Co. ) 181 - 196 2008.01 [Refereed]

　View Summary

In this paper, we deal with Cauchy problems for some quasilinear parabolic variational inequalities subject to time-dependent constraints. With re- gard to this type of problem, the authors of [8] recently developed a general theory concerned with the existence and uniqueness of solutions. The main objective of this paper is to study the key-properties of dynamical systems generated by our Cauchy problems. To this end, we first prove the well-posedness (including con- tinuous dependence) of solutions on the basis of the earlier work [8]. Eventually, we focus on the periodic situation of dynamical systems, to validate the results concerned with the existence of periodic solutions, and the asymptotic stability from the viewpoint of attractors.

DOI
Elliptic-parabolic variational inequalities with time-dependent constraints

Masahiro Kubo, Noriaki Yamazaki

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS ( AMER INST MATHEMATICAL SCIENCES ) 19 ( 2 ) 335 - 359 2007.10 [Refereed]

　View Summary

We study variational inequalities for quasilinear elliptic-parabolic equations with time-dependent constraints. Introducing a general condition for the time-dependence of convex sets defining the constraints, we establish theorems concerning existence, uniqueness as well as an order property of solutions. Some applications of the general results are given.
Nonlinear degenerate parabolic equations for a thermohydraulic model

T. Fukao, M. Kubo

Discrete and Continuous Dynamical Systems supplement 2007 399 - 408 2007.09 [Refereed]
Periodic stability of elliptic-parabolic variational inequalities with time-dependent boundary double obstacles

M. Kubo, N. Yamazaki

Discrete and Continuous Dynamical Systems supplement 2007 614 - 623 2007.09 [Refereed]
Optimal control problems for models of phase-field type with hysteresis of play operator

K.-H. Hoffmann, N. Kenmochi, M. Kubo, N.Yazamaki

Advances in Mathematical Sciences and Applications 17 ( 1 ) 305 - 336 2007.01 [Refereed]
Second order evolution equations with time-dependent subdifferentials

Masahiro Kubo

JOURNAL OF EVOLUTION EQUATIONS ( BIRKHAUSER VERLAG AG ) 7 ( 4 ) 701 - 717 2007 [Refereed]

　View Summary

We study an abstract second order nonlinear evolution equation in a real Hilbert space. We consider time-dependent convex functions and their subdifferentials operating on the first derivative of the unknown function. Introducing appropriate assumptions on the convex functions and other data, we prove the existence and uniqueness of a strong solution, and give some applications of the abstract theorem to hyperbolic variational inequalities with time-dependent constraints.

DOI
Optimal control problems for elliptic-parabolic variational inequalities with time-dependent constraints

Karl-Heinz Hoffmann, Masahiro Kubo, Noriaki Yamazaki

Numerical Functional Analysis and Optimization 27 ( 3-4 ) 329 - 356 2006.08 [Refereed]

　View Summary

In this paper, we study optimal control problems for quasi-linear elliptic-parabolic variational inequalities with time-dependent constraints. We prove the existence of an optimal control that minimizes the nonlinear cost functional. Moreover, we apply our general results to some model problems. In particular, we show the necessary condition of optimal pair for a problem of partial differential equation (PDE) with a non-homogeneous Dirichlet boundary condition. Copyright © 2006 Taylor &amp
Francis Group, LLC.

DOI
Weak solutions of a thermohydraulics model with a general nonlinear heat flux

Masahiro Kubo

GAKUTO International Series. Mathematical Sciences and Applications 23 163 - 178 2006.06 [Refereed]
Evolution equations for nonlinear degenerate parabolic PDE

M Kubo, QQ Lu

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS ( PERGAMON-ELSEVIER SCIENCE LTD ) 64 ( 8 ) 1849 - 1859 2006.04 [Refereed]

　View Summary

We define a convex function on H-1 (Omega) and characterize its subdifferential, by which we introduce an evolution equation as a weak formulation of a class of nonlinear, degenerate, singular and noncoercive parabolic PDEs associated with an arbitrary maximal monotone graph and with the Dirichlet boundary condition. (c) 2005 Elsevier Ltd. All rights reserved.

DOI
Periodic solutions of elliptic-parabolic variational inequalities with time-dependent constraints

M Kubo, N Yamazaki

JOURNAL OF EVOLUTION EQUATIONS ( BIRKHAUSER VERLAG AG ) 6 ( 1 ) 71 - 93 2006.02 [Refereed]

　View Summary

We study periodic solutions of quasilinear elliptic-parabolic variational inequalities with time-dependent constraints. Assuming that the constraint changes periodically in time, we prove existence of periodic solutions. Moreover, applications of the general results are given.

DOI
Subdifferential operator approach to the Dirichlet problem of nonlinear degenerate parabolic equations

Akio Ito, Masahiro Kubo, Quqin Lu

Differential and Difference Equations and Applications (R. P. Agarwal et al eds.), Hindawi, New York 441 - 450 2006.01 [Refereed]
Well-posedness of initial boundary value problem of degenerate parabolic equations

Masahiro Kubo

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS ( PERGAMON-ELSEVIER SCIENCE LTD ) 63 ( 5-7 ) E2629 - E2637 2005.11 [Refereed]

　View Summary

We study a nonlinear degenerate parabolic equation associated with an arbitrary maximal monotone graph. We impose initial and Dirichlet boundary conditions and prove that the problem is well-posed. (C) 2005 Elsevier Ltd. All rights reserved.

DOI
Nonlinear degenerate parabolic equations with Neumann boundary condition

M Kubo, Q Lu

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS ( ACADEMIC PRESS INC ELSEVIER SCIENCE ) 307 ( 1 ) 232 - 244 2005.07 [Refereed]

　View Summary

We study Neumann problem for a class of nonlinear degenerate parabolic PDE. A typical nonlinearity we have in mind is, for instance, β(u) = -1/u (u &GT; 0). We establish a necessary and sufficient condition on given data for existence of solution. &COPY; 2004 Elsevier Inc. All rights reserved.

DOI
Quasilinear parabolic variational inequalities with time-dependent constraints

M. Kubo, N. Yamazaki

Advances in Mathematical Sciences and Applications 15 ( 1 ) 335 - 354 2005.01 [Refereed]
A filtration model with hysteresis

M Kubo

JOURNAL OF DIFFERENTIAL EQUATIONS ( ACADEMIC PRESS INC ELSEVIER SCIENCE ) 201 ( 1 ) 75 - 98 2004.06 [Refereed]

　View Summary

We study a filtration model for which a hysteresis effect is accounted in the saturation versus pressure constitutive relation. The problem is formulated in a quasi-variational inequality. We prove the existence of a time global solution. (C) 2004 Elsevier Inc. All rights reserved.

DOI
Non-isothermal phase transition models with Neumann boundary conditions

A Ito, N Kenmochi, M Kubo

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS ( PERGAMON-ELSEVIER SCIENCE LTD ) 53 ( 7-8 ) 977 - 996 2003.06 [Refereed]

　View Summary

We study the systems of nonlinear parabolic PDEs for Penrose-Fife models of non-isothermal phase transitions. Both models with conserved and non-conserved order parameters are studied with Neumann boundary conditions imposed on the systems in multi-dimensional spatial domain. (C) 2003 Elsevier Science Ltd. All rights reserved.

DOI
Well-posedness and attractors of phase transition models with constraint

M Kubo, A Ito, N Kenmochi

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS ( PERGAMON-ELSEVIER SCIENCE LTD ) 47 ( 5 ) 3207 - 3214 2001.08 [Refereed]

　View Summary

Results and idea of proofs are presented for the well-posedness and the existence of a global attractor of the Penrose-Fife model of non-isothermal phase transitions. Models with conserved and non-conserved order parameters, on which a constraint is posed, are treated.

DOI
A phase-field model with temperature dependent constraint

P Colli, N Kenmochi, M Kubo

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS ( ACADEMIC PRESS INC ) 256 ( 2 ) 668 - 685 2001.04 [Refereed]

　View Summary

This paper is concerned with a phase-held model with temperature dependent constraint for the order parameter. In the kinetic equation of the order parameter, we take account of diffusion as well as the undercooled/superheated state which is modelled by means of a hysteresis input-output relation; the input is the temperature held and the output is the order parameter. In this paper we shall show that there exists a solution "globally" in time in a physically reasonable sense, when the coefficient of interfacial energy is sufficiently small. (C) 2001 Academic Press.

DOI
Non-isothermal phase separation models: construction of attractors.: weak well-posedness and global estimates

Akio Ito, Nobuyuki Kenmochi, Masahiro Kubo

GAKUTO International Series. Mathematical Sciences and Applications 13 137 - 152 2000.03 [Refereed]
Global attractors of phase transition models with hysteresis and diffusion effects

Noriaki Yamazaki, Masato Takahashi, Masahiro Kubo

GAKUTO International Series. Mathematical Sciences and Applications 14 460 - 471 2000.03 [Refereed]
Non-isothermal phase separation models: weak well-posedness and global estimates

Masahiro Kubo, Akio Ito, Nobuyuki Kenmochi

GAKUTO International Series. Mathematical Sciences and Applications ( Gakkotosho Co., Ltd. ) 14 311 - 323 2000.03 [Refereed]
Weak solutions of novlinear systems for non-isothermal phase transitions

N. Kenmochi, M. Kubo

Advances in Mathematical Sciences and Applications 9 ( 1 ) 499 - 521 1999.04 [Refereed]
Well-posedness for a phase-field model with constraint

N Kenmochi, M Kubo

FREE BOUNDARY PROBLEMS: THEORY AND APPLICATIONS, Chapman & Hall/CRC Res. Notes Math. ( CHAPMAN & HALL/CRC PRESS ) 409 147 - 154 1999 [Refereed]

　View Summary

A phase-field model with constraint of the Penrose-Fife type is considered. The model is a system of nonlinear parabolic PDEs which governs the (absolute) temperature and order parameter with bounded constraint. In this paper, the well-posedness of the system is shown in the product space of the dual of H-1(Omega) and L-2(Omega).
PERIODIC-SOLUTIONS FOR NONLINEAR POPULATION-DYNAMICS MODELS WITH AGE-DEPENDENCE AND SPATIAL STRUCTURE

M KUBO, M LANGLAIS

JOURNAL OF DIFFERENTIAL EQUATIONS ( ACADEMIC PRESS INC JNL-COMP SUBSCRIPTIONS ) 109 ( 2 ) 274 - 294 1994.04 [Refereed]
Periodic solutions for nonlinear population dynamics models with periodic supply

Masahiro Kubo, Michel Langlais

Pitman Research Notes in Mathematics Series 267 214 - 220 1992.01 [Refereed]
PERIODIC-SOLUTIONS FOR A POPULATION-DYNAMICS PROBLEM

M KUBO, M LANGLAIS

COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE ( GAUTHIER-VILLARS ) 313 ( 6 ) 387 - 390 1991.09 [Refereed]

　View Summary

First we consider a partial differential equation arising in population dynamics problem with age dependence and spatial structure. The birth and death processes are nonlinear, with nonlocal nonlinearities. We give existence and nonexistence results for time periodic solutions under a time periodic supply of individuals. Next we prove the existence of time periodic solutions for the corresponding S-I-R-S epidemic model.
Some variational inequalities for age-dependent population dynamics

Masahiro Kubo

Japan Journal of Industrial and Applied Mathematics 8 ( 2 ) 275 - 296 1991.06 [Refereed]

　View Summary

A variational inequality for an equation of age-dependent population diffusion is studied. A mixed-type boundary condition is prescribed on time-and age-dependent parts of the boundary. The rate of mortality is allowed to have a divergency property at the maximal age. © 1991 the JJIAM Publishing Committee.

DOI
PERIODIC-SOLUTIONS FOR A POPULATION-DYNAMICS PROBLEM WITH AGE-DEPENDENCE AND SPATIAL STRUCTURE

M KUBO, M LANGLAIS

JOURNAL OF MATHEMATICAL BIOLOGY ( SPRINGER VERLAG ) 29 ( 4 ) 363 - 378 1991 [Refereed]

　View Summary

Using a linear model with age-dependence and spatial structure we show how a periodical supply of individuals will transform an exponentially decaying distribution of population into a non-trivial asymptotically stable periodic distribution. Next we give an application to an epidemic model.
PERIODIC-SOLUTIONS OF PARABOLIC-ELLIPTIC OBSTACLE PROBLEMS

N KENMOCHI, M KUBO

JOURNAL OF DIFFERENTIAL EQUATIONS ( ACADEMIC PRESS INC ELSEVIER SCIENCE ) 88 ( 2 ) 213 - 237 1990.12 [Refereed]
Periodic solutions to porous media equations of parabolic-elliptic type

N. Kenmochi, D. Kröner, M. Kubo

Journal of Partial Differential Equations 3 ( 3 ) 63 - 77 1990.07 [Refereed]
PERIODIC STABILITY OF FLOW IN PARTIALLY SATURATED POROUS-MEDIA

N KENMOCHI, M KUBO

FREE BOUNDARY VALUE PROBLEMS, Internat. Ser. Numer. Math. ( BIRKHAUSER VERLAG ) 95 127 - 152 1990 [Refereed]
PERIODIC BEHAVIOR OF SOLUTIONS TO PARABOLIC-ELLIPTIC FREE-BOUNDARY PROBLEMS

N KENMOCHI, M KUBO

JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN ( MATH SOC JAPAN ) 41 ( 4 ) 625 - 640 1989.10 [Refereed]
Characterization of a class of evolution operators generated by time-dependent subdifferentials

M. Kubo

Funkcialaj Ekvacioj 32 ( 2 ) 301 - 321 1989.08 [Refereed]
Periodic and almost periodic stability of solutions to degenerate parabolic equations

M. Kubo

Hiroshima Mathematical Journal 19 ( 3 ) 499 - 514 1989.07 [Refereed]
Periodic behaviour of solutions to a parabolic-elliptic problem

Nobuyuki Kenmochi, Masahiro Kubo

Pitman Research Notes in Mathematics Series 208 68 - 76 1989.03 [Refereed]
Subdifferential operator approach to nonlinear age-dependent population dynamics

Masahiro Kubo

Japan Journal of Applied Mathematics 5 ( 2 ) 225 - 256 1988.06 [Refereed]

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Some obstacle problems, arising in age-dependent population dynamics, have been studied by Garroni-Lamberti [3] and Garroni-Langlais [4]. In this paper, we shall study abstract evolution equations associated with these obstacle, problems from the viewpoint of the subdifferential operator theory. Existence and uniqueness theorems will be established by using some results of the theory of evolution equations generated by time-dependent subdifferentials. Also, problems with monotone perturbations will be solved. Moreover, in the final section we apply the abstract results to two nonlinear evolution problems arising in population dynamics. © 1988 JJAM Publishing Committee.

DOI
Periodicity of solutions to some parabolic-elliptic variational inequalities

久保雅弘

非線形発展方程式と偏微分方程式数理解析研究所講究録 647 148 - 160 1988.02 [Invited]
Periodic solutions to a class of nonlinear variational inequalities with time-dependent constraints

N. Kenmochi, M. Kubo

Funkcialaj Ekvacioj 30 ( 2-3 ) 333 - 349 1987.07 [Refereed]
Periodicity and almost periodicity of solutions to free boundary problems in Hele-Shaw flows

M. Kubo

Proceedings of the Japan Academy Series A Mathematical Sciences 62 ( 8 ) 288 - 291 1986.08 [Refereed]

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Misc

ある障害物問題の時間局所・大域解と大域的アトラクターについて

深尾武史, 久保雅弘

日本数学会 2009 年度秋季総合分科会実関数論分科会アブストラクト ( 日本数学会 ) 67 - 68 2009.09
熱水力学に現れるある障害物問題の弱解と漸近挙動について

深尾武史, 久保雅弘

日本数学会 2009 年度年会実関数論分科会アブストラクト 17 - 18 2009.03
熱水力学に現れるある障害物問題の弱解と漸近挙動について

深尾武史, 久保雅弘

第34回発展方程式研究会発表論文集 53 - 54 2008.12
熱水力学に現れるある変分不等式について

深尾武史, 久保雅弘

日本数学会 2008 年度秋季総合分科会実関数論分科会アブストラクト 53 - 54 2008.09
熱水力学に現れるある変分不等式と解の正則性について

深尾武史, 久保雅弘

日本数学会 2008 年度年会実関数論分科会アブストラクト 15 - 16 2008.03
熱水力学に現れる退化放物型方程式系の可解性について

深尾武史, 久保雅弘

日本数学会 2006 年度年会実関数論分科会アブストラクト 44 - 45 2006.03

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Conference Activities & Talks

Time-dependent subdifferential evolution equations and applications to quasi-subdifferential equations

久保雅弘 [Invited]

発展方程式とその周辺 –解の定量的性質と抽象構造– 2024.10.30
Elliptic-parabolic quasi-variational evolution equations

久保雅弘, 山崎教昭

日本数学会2023年度秋季総合分科会 2023.09.23
（企画特別講演）時間依存劣微分発展方程式と準変分発展方程式

久保雅弘 [Invited]

日本数学会2022年度年会 2022.03.30
Elliptic-parabolic quasi-subdifferential evolution equations

Masahiro Kubo [Invited]

Workshop on Mathematical Methods and Applications with Nonlinear Evolution Equations 2019.08.17
Quasi-variational principles and quasi-subdifferential operators

Masahiro Kubo [Invited]

The 5th Polish Japanese Days on Nonlinear Analysis in Interdisciplinary Sciences - Modellings, Theory and Simulations - 2012.11
A new class of nonlinear evolution equations

Masahiro Kubo [Invited]

The 9th AIMS Conference on Dynnamical Systems, Differential Equations and Applications 2012.07
（特別講演）非線形発展方程式と変分不等式の特異摂動,

久保雅弘 [Invited]

日本数学会2009年度秋季総合分科会 2009.09.25
A class of quasi-variational inequalities for hysteresis

Masahiro Kubo [Invited]

The 6th AIMS Conference on Dynnamical Systems, Differential Equations and Applications 2006.06.25
Subdifferential operator approach to a class of nonlinear degenerate parabolic equations

Masahiro Kubo [Invited]

Conference on Differential & Difference Equations 2005.08.01
Weak solutions of the Boussinesq system with nonlinear degenerate heat flux

Masahiro Kubo [Invited]

The 3rd Polish Japanese Days "Mathematical Approach to Nonlinear Phenomena" 2004.11.30
Initial boundary value problems of nonlinear degenerate parabolic equations

Masahiro Kubo [Invited]

The 4th World Congress of Nonlinear Analysts 2004.07.05
Attractors of phase transition models with constraint

Masahiro Kubo [Invited]

The 3rd World Congress of Nonlinear Analysts 2000.07
Periodicity of saturated-unsaturated flow in porous medium

Masahiro Kubo [Invited]

Freie Randwertaufgaben 1989.07

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KAKENHI

非線形発展方程式と準変分解析

2014.04

-

2019.03

Grant-in-Aid for Scientific Research(C) Principal investigator

Committee member history in academic associations, government agencies, municipalities, etc.

委員

2024.03.01

-

2025.02.28

日本数学会

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学協会、政府、自治体等の公的委員

代議員（阪神地区）,任期:1年
委員

2022.03

-

2023.02

日本数学会

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学協会、政府、自治体等の公的委員

代議員（阪神地区）,任期:1年
委員

2018.03

-

2019.02

日本数学会

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学協会、政府、自治体等の公的委員

代議員（阪神地区）,任期:1年
委員

2016.03

-

2017.02

日本数学会

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学協会、政府、自治体等の公的委員

代議員（阪神地区）,任期:1年