Takayama, Masahiro

写真a

Affiliation

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

Position

Research Associate/Assistant Professor/Instructor

Profile Summary 【 Display / hide

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
    -
    Present

    明治大学理工学部, 非常勤講師

Academic Background 【 Display / hide

  • 1993.03

    Kanazawa University, Faculty of Science

    University, Graduated

  • 1995.03

    Osaka University, Graduate School, Division of Natural Science, 数学専攻

    Graduate School, Completed, Master's course

  • 2000.03

    Osaka University, Graduate School, Division of Natural Science, 数学専攻

    Graduate School, Completed, Doctoral course

Academic Degrees 【 Display / hide

  • 理学, Osaka University, 2000.03

 

Research Areas 【 Display / hide

  • Natural Science / Basic analysis (Basic Analysis)

  • Natural Science / Mathematical analysis

 

Papers 【 Display / hide

  • The Kinetic and Hydrodynamic Bohm Criteria for Plasma Sheath Formation

    Suzuki M., Takayama M.

    Archive for Rational Mechanics and Analysis (Archive for Rational Mechanics and Analysis)  247 ( 5 )  2023.10

    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.

  • Double Layer Solutions of the Vlasov–Poisson System

    Suzuki M., Takayama M.

    Springer Proceedings in Mathematics and Statistics (Springer Proceedings in Mathematics and Statistics)  429   41 - 52 2023

    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.

  • Stability and Existence of Stationary Solutions to the Euler–Poisson Equations in a Domain with a Curved Boundary

    Suzuki M., Takayama M.

    Archive for Rational Mechanics and Analysis (Archive for Rational Mechanics and Analysis)  239 ( 1 ) 357 - 387 2021.01

    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

    Masahiro Takayama

    Osaka J. Math. 55   547 - 565 2018

    Research paper (scientific journal), Accepted

  • Long-time behavior of solutions to an outflow problem for a shallow water model

    Bongsuk Kwon, Masahiro Suzuki, Masahiro Takayama

    J. Differential Equations 255   1883 - 1905 2013

    Joint Work, Accepted

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

Presentations 【 Display / hide

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

    Masahiro Takayama

    The 4th Workshop on recent development of mathematical fluid dynamics and hyperbolic conservation laws (National Taiwan University) , 

    2019.12

    Oral presentation (general)

  • 吊り下げられた紐の方程式に対する初期境界値問題

    TAKAYAMA MASAHIRO

    現象解析特別セミナー第10回(宮崎大学) (宮崎大学) , 

    2016.09

    Oral presentation (general)

  • Initial boundary value problem for the equation of suspended string

    TAKAYAMA MASAHIRO

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

    2016.07

    Oral presentation (general)

  • 吊り下げられた紐の運動のモデル

    TAKAYAMA MASAHIRO

    現象解析特別セミナー第3回(群馬大学) (群馬大学) , 

    2013.03

    Oral presentation (general)

  • 紐の運動に現れる退化双曲型方程式の初期境界値問題

    TAKAYAMA MASAHIRO

    微分方程式セミナー(大阪大学) (大阪大学) , 

    2010.05

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

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Courses Taught 【 Display / hide

  • FOUNDATION FOR MATHEMATICAL SCIENCE 3

    2023

  • FOUNDATION FOR MATHEMATICAL SCIENCE 2

    2023

  • COMPLEX ANALYSIS 1 AND EXERCISE

    2023

  • FUNCTIONAL EQUATIONS 1 AND ITS EXERCISE

    2023

  • FUNCTIONAL EQUATIONS 1 AND ITS EXERCISE

    2022

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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