井口 達雄 (イグチ タツオ)

Iguchi, Tatsuo

写真a

所属(所属キャンパス)

理工学部 数理科学科 (矢上)

職名

教授

HP

外部リンク

経歴 【 表示 / 非表示

  • 1997年01月
    -
    2002年03月

    九州大学大学院数理学研究科文部教官助手

  • 2002年04月
    -
    2006年03月

    東京工業大学大学院理工学研究科文部科学教官助教授

  • 2006年04月
    -
    2011年03月

    慶應義塾大学理工学部助教授

  • 2011年04月
    -
    継続中

    慶應義塾大学理工学部教授

学歴 【 表示 / 非表示

  • 1993年03月

    早稲田大学, 理工学部, 数学科

    大学, 卒業

  • 1995年04月

    早稲田大学, 理工学研究科, 数理科学専攻

    大学院, 修了, 修士

  • 1996年12月

    早稲田大学, 理工学研究科, 数理科学専攻

    大学院, 退学, 博士

学位 【 表示 / 非表示

  • On the Well-Posedness of Initial Value Problems for Ideal Fluid with Free Boundary, 早稲田大学, 論文, 1998年03月

 

研究分野 【 表示 / 非表示

  • 自然科学一般 / 基礎解析学 (基礎解析学)

  • 自然科学一般 / 数理解析学 (大域解析学)

 

論文 【 表示 / 非表示

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

    Iguchi T., Takayama M.

    Mathematische Annalen (Mathematische Annalen)  2024年

    ISSN  00255831

     概要を見る

    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.

  • A mathematical analysis of the Kakinuma model for interfacial gravity waves. Part I: Structures and well-posedness

    Duchêne V., Iguchi T.

    Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire (Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire)  41 ( 2 ) 257 - 315 2024年

    ISSN  02941449

     概要を見る

    We consider a model, which we named the Kakinuma model, for interfacial gravity waves. As is well known, the full model for interfacial gravity waves has a variational structure whose Lagrangian is an extension of Luke’s Lagrangian for surface gravity waves, that is, water waves. The Kakinuma model is a system of Euler–Lagrange equations for approximate Lagrangians, which are obtained by approximating the velocity potentials in the Lagrangian for the full model. In this paper we first analyze the linear dispersion relation for the Kakinuma model and show that the dispersion curves highly fit that of the full model in the shallow water regime. We then analyze the linearized equations around constant states and derive a stability condition, which is satisfied for small initial data when the denser water is below the lighter water. We show that the initial value problem is in fact well posed locally in time in Sobolev spaces under the stability condition, the noncavitation assumption, and intrinsic compatibility conditions, in spite of the fact that the initial value problem for the full model does not have any stability domain so that its initial value problem is ill posed in Sobolev spaces. Moreover, it is shown that the Kakinuma model enjoys a Hamiltonian structure and has conservative quantities: mass, total energy, and in the case of a flat bottom, momentum.

  • A mathematical analysis of the Kakinuma model for interfacial gravity waves. Part II: Justification as a shallow water approximation

    Duchêne V., Iguchi T.

    Proceedings of the Royal Society of Edinburgh Section A: Mathematics (Proceedings of the Royal Society of Edinburgh Section A: Mathematics)  2024年

    ISSN  03082105

     概要を見る

    We consider the Kakinuma model for the motion of interfacial gravity waves. The Kakinuma model is a system of Euler-Lagrange equations for an approximate Lagrangian, which is obtained by approximating the velocity potentials in the Lagrangian of the full model. Structures of the Kakinuma model and the well-posedness of its initial value problem were analysed in the companion paper [14]. In this present paper, we show that the Kakinuma model is a higher order shallow water approximation to the full model for interfacial gravity waves with an error of order in the sense of consistency, where and are shallowness parameters, which are the ratios of the mean depths of the upper and the lower layers to the typical horizontal wavelength, respectively, and is, roughly speaking, the size of the Kakinuma model and can be taken an arbitrarily large number. Moreover, under a hypothesis of the existence of the solution to the full model with a uniform bound, a rigorous justification of the Kakinuma model is proved by giving an error estimate between the solution to the Kakinuma model and that of the full model. An error estimate between the Hamiltonian of the Kakinuma model and that of the full model is also provided.

  • Hyperbolic free boundary problems and applications to wave-structure interactions

    Iguchi T., Lannes D.

    Indiana University Mathematics Journal (Indiana University Mathematics Journal)  70 ( 1 ) 353 - 464 2021年

    研究論文(学術雑誌), 共著, 査読有り,  ISSN  00222518

     概要を見る

    Motivated by a new kind of initial boundary value problem (IBVP) with a free boundary arising in wave-structure interaction, we propose here a general approach to one-dimensional IBVP as well as transmission problems. For general strictly hyperbolic N × N quasilinear hyperbolic systems, we derive new sharp linear estimates with refined dependence on the source term and control on the traces of the solution at the boundary. These new estimates are used to obtain sharp results for quasilinear IBVP and transmission problems, and we also use them to propose a general approach to 2 × 2 quasilinear IBVP and transmission problems with a moving or possibly free boundary. In the latter case, two kinds of evolution equations for the boundary are considered. The first one is of “kinematic type” in the sense that the velocity of the interface has the same regularity as the trace of the solution. Several applications that fall into this category are considered: the interaction of waves with a lateral piston, and a new version of the well-known stability of shocks (classical and undercompressive) that improves the results of the general theory by taking advantage of the specificities of the one-dimensional case. We also consider “fully nonlinear” evolution equations characterized by the fact that the velocity of the interface is one derivative more singular than the trace of the solution. This configuration is the most challenging; it is motivated by a free boundary problem arising in wave-structure interaction: namely, the evolution of the contact line between a floating object and the water. This problem is solved as an application of the general theory developed here.

  • Isobe-Kakinuma model for water waves

    T. Iguchi

    Mathematics for Industry (Springer)  34   181 - 191 2020年08月

    研究論文(国際会議プロシーディングス), 単著, 査読有り

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KOARA(リポジトリ)収録論文等 【 表示 / 非表示

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研究発表 【 表示 / 非表示

  • A mathematical analysis of the Kakinuma model for interfacial gravity waves

    井口達雄

    RIMS共同研究(公開型)「流体と気体の数学解析」 (京都大学数理解析研究所 (online)) , 

    2021年07月

    口頭発表(一般)

  • A Hamiltonian structure of the Isobe-Kakinuma model for water waves

    Tatsuo Iguchi

    Workshop on Free Surface Hydrodynamics (The Fields Institute for Research in Mathmatical Sciences (online)) , 

    2020年10月

    口頭発表(招待・特別)

  • 磯部‐柿沼モデルの孤立波解とその極限波

    井口達雄

    海洋・海岸における波動の解析モデルの発展 (九州大学応用力学研究所) , 

    2019年12月

    口頭発表(一般)

  • Initial value problem to a shallow water model with a floating solid body

    井口達雄

    神戸大学解析セミナー (神戸大学理学部) , 

    2019年11月

    公開講演,セミナー,チュートリアル,講習,講義等

  • Initial value problem to a shallow water model with a floating solid body

    井口達雄

    九州関数方程式セミナー (福岡大学セミナーハウス) , 

    2019年11月

    公開講演,セミナー,チュートリアル,講習,講義等

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競争的研究費の研究課題 【 表示 / 非表示

  • 水の波の数学解析の新展開

    2022年04月
    -
    2027年03月

    文部科学省・日本学術振興会, 科学研究費助成事業, 井口 達雄, 基盤研究(B), 補助金,  研究代表者

  • 水の波の新しいモデルの創出とその数学解析

    2017年06月
    -
    2020年03月

    文部科学省・日本学術振興会, 科学研究費助成事業, 井口 達雄, 挑戦的研究(萌芽), 補助金,  研究代表者

受賞 【 表示 / 非表示

  • IOP Outstanding Reviewer Awards 2018 (Nonlinearity)

    2019年03月

    受賞区分: 学会誌・学術雑誌による顕彰

  • 日本数学会 函数方程式論分科会 福原賞

    井口 達雄, 2010年12月, 水面波方程式の数学解析の研究

    受賞区分: 国内学会・会議・シンポジウム等の賞

  • 手島工業教育資金団藤野研究賞

    井口 達雄, 2003年03月, 水面波の方程式の解析的研究

    受賞区分: 出版社・新聞社・財団等の賞

 

担当授業科目 【 表示 / 非表示

  • 関数方程式特論A

    2024年度

  • 関数方程式概論

    2024年度

  • 数学2B

    2024年度

  • 数学2A

    2024年度

  • 数学1B

    2024年度

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所属学協会 【 表示 / 非表示

  • 日本数学会, 

    1994年
    -
    継続中