Takayama, Masahiro

写真a

Affiliation

Faculty of Science and Technology, Department of Mathematics （Yagami）

Position

Research Associate/Assistant Professor/Instructor
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Profile Summary 【 Display / hide 】

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Career 【 Display / hide 】

  • 2000.04
    -
    2001.03

    大阪大学大学院理学研究科, 教務補佐員

  • 2000.04
    -
    2001.03

    大阪電気通信大学工学部第1部, 非常勤講師

  • 2001.04
    -
    2007.03

    慶應義塾大学理工学部数理科学科, 助手

  • 2007.04
    -
    Present

    慶應義塾大学理工学部数理科学科, 助教

  • 2009.04
    -
    2018.03

    明治大学理工学部, 非常勤講師

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Academic Background 【 Display / hide 】

  • 1989.04
    -
    1993.03

    Kanazawa University, 理学部

    University, Graduated

  • 1993.04
    -
    1995.03

    Osaka University, 理学研究科, 数学専攻

    Graduate School, Completed, Master's course

  • 1995.04
    -
    2000.03

    Osaka University, 理学研究科, 数学専攻

    Graduate School, Completed, Master's course

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Academic Degrees 【 Display / hide 】

  • 理学, Osaka University, 2000.03

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Matters concerning Career Achievements 【 Display / hide 】

  • 2001.04
    -
    Present

    数理科学科セミナーノート編集委員

  • 2017.04
    -
    Present

    数理科学科図書委員

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Research Areas 【 Display / hide 】

  • Natural Science / Basic analysis (Basic Analysis)

  • Natural Science / Mathematical analysis

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Research Keywords 【 Display / hide 】

  • degenerate hyperbolic equation, motion of a string

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Research Themes 【 Display / hide 】

  • 紐の運動の研究, 

    2006
    -
    Present

    　View Summary

    吊り下げられた紐の運動に対する初期境界値問題の適切性について研究を行っている。

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Papers 【 Display / hide 】

  • A priori estimates for solutions to equations of motion of an inextensible hanging string

    Iguchi T., Takayama M.

    Math. Ann.   2024

    Research paper (scientific journal), Accepted,  ISSN  00255831

    　View Summary

    We consider the initial boundary value problem to equations of motion of an inextensible hanging string of finite length under the action of the gravity. We also consider the problem in the case without any external forces. In this problem, the tension of the string is also an unknown quantity. It is determined as a unique solution to a two-point boundary value problem, which is derived from the inextensibility of the string together with the equation of motion, and degenerates linearly at the free end. We derive a priori estimates for solutions to the initial boundary value problem in weighted Sobolev spaces under a natural stability condition. The necessity for the weights results from the degeneracy of the tension. Uniqueness of solutions is also proved.

  • Double layer solutions of the Vlasov--Poisson system

    Suzuki M., Takayama M.

    Gas dynamics with applications in industry and life sciences （Springer, Cham)     41 - 52 2023

    Research paper (international conference proceedings), Accepted,  ISSN  21941009

    　View Summary

    We consider the boundary value problem of the stationary Vlasov–Poisson system in a half line. In another paper, we clarified completely when there is a single layer solution, that is a solution whose electrostatic potential is monotone. In this paper, we study the possibility of the existence of double layer solutions whose electrostatic potential has a unique critical point and extremum.

  • The kinetic and hydrodynamic Bohm criteria for plasma sheath formation

    Suzuki M., Takayama M.

    Arch. Ration. Mech. Anal. 247   86 2023

    Research paper (scientific journal), Accepted,  ISSN  00039527

    　View Summary

    The purpose of this paper is to mathematically investigate the formation of a plasma sheath, and to analyze the Bohm criteria which are required for the formation. Bohm originally derived the (hydrodynamic) Bohm criterion from the Euler–Poisson system. Boyd and Thompson proposed the (kinetic) Bohm criterion from a kinetic point of view, and then Riemann derived it from the Vlasov–Poisson system. In this paper, we prove the solvability of boundary value problems of the Vlasov–Poisson system. In the process, we see that the kinetic Bohm criterion is a necessary condition for the solvability. The argument gives a simpler derivation of the criterion. Furthermore, the hydrodynamic criterion can be derived from the kinetic criterion. It is of great interest to find the relation between the solutions of the Vlasov–Poisson and Euler–Poisson systems. To clarify the relation, we also study the delta mass limit of solutions of the Vlasov–Poisson system.

  • Stability and existence of stationary solutions to the Euler--Poisson equations in a domain with a curved boundary

    Suzuki M., Takayama M.

    Arch. Ration. Mech. Anal. 239   357 - 387 2021

    Research paper (scientific journal), Accepted,  ISSN  00039527

    　View Summary

    The purpose of this paper is to mathematically investigate the formation of a plasma sheath near the surface of walls immersed in a plasma, and to analyze qualitative information of such a sheath layer. In the case of planar wall, Bohm proposed a criterion on the velocity of the positive ion for the formation of sheath, and several works gave its mathematical validation. It is of more interest to analyze the criterion for the nonplanar wall. In this paper, we study the existence and asymptotic stability of stationary solutions for the Euler–Poisson equations in a domain of which boundary is drawn by a graph. The existence and stability theorems are shown by assuming that the velocity of the positive ion satisfies the Bohm criterion at infinite distance. What most interests us in these theorems is that the criterion together with a suitable necessary condition guarantees the formation of sheaths as long as the shape of walls is drawn by a graph.

  • Initial--boundary value problem for the degenerate hyperbolic equation of a hanging string

    Takayama M.

    Osaka J. Math. 55   547 - 565 2018

    Research paper (scientific journal), Accepted

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Papers, etc., Registered in KOARA 【 Display / hide 】

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Presentations 【 Display / hide 】

  • A priori estimates for solutions to equations of motion of an inextensible hanging string

    Takayama M.

    流体と気体の数学解析（京都大学数理解析研究所） (京都大学益川ホール) , 

    2024.06
    , 

    Oral presentation (general)

  • A priori estimates for solutions to equations of motion of an inextensible hanging string

    高山正宏

    非線形解析セミナー（慶應義塾大学） (慶應義塾大学) , 

    2024.06
    , 

    Public lecture, seminar, tutorial, course, or other speech

  • 吊り下げられた紐の運動に対する解のアプリオリ評価

    高山正宏, 井口達雄

    日本数学会（大阪公立大学） (大阪公立大学) , 

    2024.03
    , 

    Oral presentation (general)

  • Vlasov-Poisson方程式の定常解の安定性・不安定性

    鈴木政尋, 高山正宏, Zhang K. Z.

    日本数学会（中央大学） (中央大学) , 

    2023.03
    , 

    Oral presentation (general)

  • プラズマ境界層の安定性と不安定性について

    鈴木政尋, 高山正宏, Zhang K. Z.

    OCAMI研究集会「渦と磁場」（博多シティ） (博多シティ) , 

    2022.12
    , 

    Oral presentation (invited, special)

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Courses Taught 【 Display / hide 】

  • FUNCTIONAL EQUATIONS 1 AND ITS EXERCISE

    2024

  • FOUNDATION FOR MATHEMATICAL SCIENCE 3

    2024

  • FOUNDATION FOR MATHEMATICAL SCIENCE 2

    2024

  • COMPLEX ANALYSIS 1 AND EXERCISE

    2024

  • FUNCTIONAL EQUATIONS 1 AND ITS EXERCISE

    2023

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Courses Previously Taught 【 Display / hide 】

  • 数理解析同演習

    Keio University

    2018.04
    -
    2019.03
    , 

    Spring Semester, Seminar

  • 関数方程式第１同演習

    Keio University

    2018.04
    -
    2019.03
    , 

    Autumn Semester, Seminar

  • 実解析第１同演習

    Keio University

    2018.04
    -
    2019.03
    , 

    Spring Semester, Seminar

  • 基礎数学３

    明治大学理工学部

    2018.04
    -
    2019.03

  • 基礎数学４

    明治大学理工学部

    2018.04
    -
    2019.03

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Memberships in Academic Societies 【 Display / hide 】

  • 日本数学会, 

    1996.04
    -
    Present
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