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Mathematical Analysis of various nonlinear problems for phenomena in continua

Research Project

Project/Area Number 18340042
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section一般
Research Field Basic analysis
Research InstitutionKeio University

Principal Investigator

TANI Atusi  Keio University, 理工学部, 教授 (90118969)

Co-Investigator(Kenkyū-buntansha) MAEJIMA Makoto  慶應義塾大学, 理工学部, 教授 (90051846)
SHIMOMURA Shun  慶應義塾大学, 理工学部, 教授 (00154328)
NODERA Takashi  慶應義塾大学, 理工学部, 教授 (50156212)
TAMURA Akihisa  慶應義塾大学, 理工学部, 教授 (50217189)
YOSHIZAWA Masatsugu  慶應義塾大学, 理工学部, 教授 (10095664)
ISHIKAWA Shiro  慶應義塾大学, 理工学部, 准教授 (10051913)
IGUCHI Tatsuo  慶應義塾大学, 理工学部, 准教授 (20294879)
TAKAYAMA Masahiro  慶應義塾大学, 理工学部, 助教 (90338252)
SUGIURA Toshihiko  慶應義塾大学, 理工学部, 准教授 (70265932)
伊藤 成治  弘前大学, 教育学部, 教授 (40193487)
田中 尚人  福岡大学, 理学部, 助教授 (00247222)
伊藤 弘道  群馬大学, 工学部, 助手 (30400790)
Co-Investigator(Renkei-kenkyūsha) ITOH Shigeharu  弘前大学, 教育学部, 教授 (40193487)
TANAKA Naoto  福岡大学, 理学部, 准教授 (00247222)
ITOU Hiromichi  群馬大学, 工学部, 助教 (30400790)
Project Period (FY) 2006 – 2008
Project Status Completed (Fiscal Year 2008)
Budget Amount *help
¥10,090,000 (Direct Cost: ¥8,500,000、Indirect Cost: ¥1,590,000)
Fiscal Year 2008: ¥3,510,000 (Direct Cost: ¥2,700,000、Indirect Cost: ¥810,000)
Fiscal Year 2007: ¥3,380,000 (Direct Cost: ¥2,600,000、Indirect Cost: ¥780,000)
Fiscal Year 2006: ¥3,200,000 (Direct Cost: ¥3,200,000)
KeywordsNavier-Stokes equations / Stokes equations / water waves / free boundary problem / slip boundary conditions / crack problem / domain with piecewise continuous boundary / Navier slip condition / sector domain / stability / 国際研究者交流 / ロシア:アメリカ:ポーランド / global solution / self-gravitation / radiative and reactive gas / piecewise smooth boundary / overlapping domain problem / inhomogeneous fluid-like body / Navier Stokes equations / sector / shape derivative / nonlinear parabolic system
Research Abstract

連続体および連続体近似できる自然現象の数理モデル方程式を数学解析し, 次のような研究成果が得られた(主要なもののみ記す).
(1) Navier-Stokes方程式, Stokes 方程式に対して, 区分的に連続な境界を持つ領域, 角領域での強解の一意存在 ; (2) Navier-Stokes方程式に対して, 滑り境界条件(Navier型, 閾値型) 下での強解の一意存在 ; (3) 水の波(渦なし非圧縮Euler方程式の自由境界問題) の長波近似, 浅水波近似の正当化 ; (4) 自己重力作用下での流体星(化学的に活性な圧縮性粘性流体) の1次元問題および3次元球対称問題の滑らかな時間大域解の一意存在 ; (5) 弾性体に対するいくつかの亀裂問題の可解性.

Report

(4 results)
  • 2008 Annual Research Report   Final Research Report ( PDF )
  • 2007 Annual Research Report
  • 2006 Annual Research Report
  • Research Products

    (44 results)

All 2009 2008 2007 2006

All Journal Article (37 results) (of which Peer Reviewed: 31 results) Presentation (7 results)

  • [Journal Article] On some boundary value problem for the Stokes equations with a parameter in an infinite sector2009

    • Author(s)
      S. Itoh, N. Tanaka and A. Tani
    • Journal Title

      To appear in the special volume of the series"Advances in Mathematical Fluid Mechanics" dedicated to the memory of Professor Alexander Kazhikhov edited by A. Fursikov, G.P. Galdi and V.V. Puchnachov, Birkhauser

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] An Adaptive Gradient Smoothing Method(GSM) For Fluid Dynamics Problems2009

    • Author(s)
      X.-X. Guo, G.-R. Liu and A. Tani
    • Journal Title

      To appear in Intern. J. Numer. Meth. Fluids

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] A shallow water approxima-tion for water waves2009

    • Author(s)
      T. Iguchi
    • Journal Title

      to appear in J. Math. Kyoto Univ.

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Some estimates of pressure for the Stokes equations in an infinite sector2009

    • Author(s)
      S. Itoh, N. Tanaka and A. Tani
    • Journal Title

      Proc. Japan Acad. 85, Ser. A

      Pages: 37-40

    • NAID

      40016557929

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Steady solution and its stability to Navier-Stokes equations with general Navier slip boundary condition2009

    • Author(s)
      S. Itoh, N. Tanaka and A. Tani
    • Journal Title

      Zap. Nauchn. Semin. POMI 362

      Pages: 153-175

    • NAID

      120006459356

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] A two-phase problem for capillary-gravity waves and the Benjamin-Ono quation2009

    • Author(s)
      K. Ohi and T. Iguchi
    • Journal Title

      Discrete Contin. Dyn. Syst. 23

      Pages: 1205-1240

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Steady solution and its stability to Navier-Stokes equations with general Navier slip boundary condition2009

    • Author(s)
      S. Itoh
    • Journal Title

      Zap. Nauchn. Semin. POMI 362

      Pages: 153-175

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Some estimates of pressure for the Stokes equations in an infinite sector2009

    • Author(s)
      S. Itoh
    • Journal Title

      Proc. Japan Acad. 85

      Pages: 37-40

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Global solvability of the free-boundary problem for one-dimensional motion of a self-gravitating viscous radiative and reactive gas2008

    • Author(s)
      M. Umehara and A. Tani
    • Journal Title

      Proc. Japan Acad. 84, Ser. A

      Pages: 122-127

    • NAID

      40016292880

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Evolution of a crack with kink And non-penetration2008

    • Author(s)
      A. M. Khludnev, V. A. Kovtunenko and A. Tani
    • Journal Title

      J. Math. Soc. Japan 60

      Pages: 1219-1253

    • NAID

      10024905407

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Unilateral contact problems for two inclined elastic bodies2008

    • Author(s)
      A. M. Khludnev and A. Tani
    • Journal Title

      Europ. J. Mech. A-Solids 27

      Pages: 365-377

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Overlapping domain problems in the crack theory with possible contact between crack faces2008

    • Author(s)
      A. M. Khludnev and A. Tani
    • Journal Title

      Quart. Appl. Math. 66

      Pages: 423-435

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Global solution to the equations for a spherically symmetric viscous radiative and reactive gas over the rigid core2008

    • Author(s)
      M. Umehara and A. Tani
    • Journal Title

      Anal. Appl. 6

      Pages: 183-211

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Enclosure method and reconstruction of linear crack in an elastic body2008

    • Author(s)
      M. Ikehata and H. Itou
    • Journal Title

      J. Phys. : Confer. Series. 135

      Pages: 12052-12059

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] An inverse problem for a linear crack in an anisotropic elastic body and the enclosure method2008

    • Author(s)
      M. Ikehata and H. Itou
    • Journal Title

      Inverse Problems 24

      Pages: 25005-2525

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Evolution of a crack with kink and non-penetration2008

    • Author(s)
      A. M. Khludnev
    • Journal Title

      J. Math. Soc. Japan 60

      Pages: 1219-1253

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Global solution to the equations for a spherically symmetric viscous radiative and reactive gas over the rigid core2008

    • Author(s)
      M. Umehara and A. Tani
    • Journal Title

      Analysis and Applications 8,(掲載決定)

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Overlapping domain problems in the crack theory with possible contact between crack faces2008

    • Author(s)
      A. M. Khludnev and A. Tani
    • Journal Title

      Quart.J.Appl.Math (掲載決定)

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Steady Navier-Stokes equations in a domain with piecewise smooth boundary. Comput2007

    • Author(s)
      S. Itoh, N. Tanaka and A. Tani
    • Journal Title

      Math. Appl. 53

      Pages: 685-691

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Global solution to the one-dimensional equations for a self-gravitating viscous radiative and reactive gas2007

    • Author(s)
      M. Umehara and A. Tani
    • Journal Title

      J. Differential Equations 234

      Pages: 439-463

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Steady solutions of the Navier--Stokes equations with threshold slip boundary conditions2007

    • Author(s)
      C. Le Roux and A. Tani
    • Journal Title

      Math. Methods Appl. Sci. 30

      Pages: 595-624

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] A long wave approximation for capillary-gravity waves and the Kawahara equation2007

    • Author(s)
      T. Iguchi
    • Journal Title

      Bull. Inst. Math. Acad. Sin. (N.S.) 2

      Pages: 179-220

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] A long wave approximation for capillary-gravity waves and an effect of the bottom2007

    • Author(s)
      T. Iguchi
    • Journal Title

      Comm. Partial Differential Equations 32

      Pages: 37-85

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Reconstruction of a linear crack in an anisotropic elastic body from a single set of measured data2007

    • Author(s)
      M. Ikehata and H. Itou
    • Journal Title

      Inverse Problems 23

      Pages: 589-607

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Steady Navier-Stokes equations in a domain with piecewise smooth boundary2007

    • Author(s)
      S. Itoh, N. Tanaka and A. Tani
    • Journal Title

      Comput.Math.Appl 53

      Pages: 685-691

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A long wave approximation for capillary-gravity waves and an effect of the bottom2007

    • Author(s)
      T. Iguchi
    • Journal Title

      Comm.Partial Differential Equations 32

      Pages: 37-85

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Usage of the convergence test of the residual norm in Tsuno-Nodera version of the GMRES algorithm2007

    • Author(s)
      K. Moriya and T. Nodera
    • Journal Title

      ANZTAM J 49

      Pages: 209-308

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Steady solutions of the Navier…Stokes equations with threshold slipboundary conditions2007

    • Author(s)
      C.Le Roux, A.Tani
    • Journal Title

      Math. Methods Appl. Sci. 30

      Pages: 595-624

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Global solution to the one-dimensional equations for a self-gravitating viscous radiative and reactive gas2007

    • Author(s)
      M.Umehara, A.Tani
    • Journal Title

      J. Differential Equations 234

      Pages: 439-463

    • Related Report
      2006 Annual Research Report
  • [Journal Article] On some boundary value problem for the Stokes equations in an infinite sector2006

    • Author(s)
      S. Itoh, N. Tanaka and A. Tani
    • Journal Title

      Anal. Appl. 4

      Pages: 357-375

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Shape derivative of energy functional in an infinite elastic strip with a semi-infinite cracks2006

    • Author(s)
      H. Itou and A. Tani
    • Journal Title

      Tokyo J. Math. 29

      Pages: 385-397

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Finite difference schemes for a certain nonlinear parabolic system2006

    • Author(s)
      H. Morioka and A. Tani
    • Journal Title

      Math. Models Meth. Appl. Sci. 16

      Pages: 679-699

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] A mathematical justification of the forced Korteweg-de Vries equation for capillary-gravity waves2006

    • Author(s)
      T. Iguchi
    • Journal Title

      Kyushu J. Math. 60

      Pages: 267-303

    • NAID

      130000063141

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Finite difference schemes for a certain nonlinear parabolic system2006

    • Author(s)
      H.Morioka, A.Tani
    • Journal Title

      Math. Models Meth. Appl. Sci. 16

      Pages: 679-699

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Shape derivative of energy functional in an infinite elastic strip with a semi-infinite cracks2006

    • Author(s)
      H.Itou, A.Tani
    • Journal Title

      Tokyo J. 29

      Pages: 385-397

    • Related Report
      2006 Annual Research Report
  • [Journal Article] On some boundary value problem for the Stokes equations in an infinite sector2006

    • Author(s)
      S.Itoh, N.Tanaka, A.Tani
    • Journal Title

      Analysis Appl. 4

      Pages: 357-375

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Global solution to the one-dimensional model equations for viscous liquid stars in reactive and combustion processes2006

    • Author(s)
      M.Umehara, A.Tani
    • Journal Title

      RIMS Kokyuroku 1496

      Pages: 78-84

    • Related Report
      2006 Annual Research Report
  • [Presentation] The Stokes equations in a domain with piecewise smooth boundary2008

    • Author(s)
      A. Tani
    • Organizer
      International Conference on"Differential equations, Function spaces, Approximation theory" dedicated to 100th anniversary of the birthday of Sergei L. Sobolev
    • Place of Presentation
      Novosibirsk, Russia
    • Year and Date
      2008-10-10
    • Related Report
      2008 Final Research Report
  • [Presentation] The Stokes equations in a domain with piecewise smoothboundary2008

    • Author(s)
      A. Tani
    • Organizer
      International Conference on "Differential equations, Function spaces, Approximation theory" dedicated to 100th anniversary of the birthday of Sergei L. Sobolev
    • Place of Presentation
      Novosibirsk, Russia
    • Year and Date
      2008-10-10
    • Related Report
      2008 Annual Research Report
  • [Presentation] Initial-boundary value problem for the motion of incompressible inhomogeneous fluid-like bodies2008

    • Author(s)
      A. Tani
    • Organizer
      Parabolic and Navier-Stokes Equations 2008 in honour of V.A. Solonnikov
    • Place of Presentation
      Mathematical Research and Conference Center, Bedlewo, Poland
    • Year and Date
      2008-09-01
    • Related Report
      2008 Final Research Report
  • [Presentation] Temporally Global Solution to the Equations for a Spherically Symmetric Viscous Radiative and Reactive Gas over the Rigid Core2008

    • Author(s)
      A. Tani
    • Organizer
      International Conference on ``Modern problems of Mathematical Modelling and Computational Technologies-2008
    • Place of Presentation
      Krasnoyarsk, Russia
    • Year and Date
      2008-08-22
    • Related Report
      2008 Final Research Report
  • [Presentation] Initial boundary value problem for the resistive drift wave turbulence2007

    • Author(s)
      A. Tani
    • Organizer
      International Conference on"Inverse and Ill-posed problems of Mathematical Physics" dedicated to Professor M.M. Lavrent'ev on occasion of his 75-th birthday
    • Place of Presentation
      Novosibirsk, Russia
    • Year and Date
      2007-08-23
    • Related Report
      2008 Final Research Report
  • [Presentation] Initial boundary value problem for the resistive driftwave turbulence2007

    • Author(s)
      A. Tani
    • Organizer
      International Conference on"Inverse and Ill-posed problems of Mathematical Physics"
    • Place of Presentation
      Novosibirsk(Russia)
    • Year and Date
      2007-08-23
    • Related Report
      2007 Annual Research Report
  • [Presentation] Mathematical problems for the primitive equations2006

    • Author(s)
      A. Tani
    • Organizer
      Workshop on Mathematical Analysis on Nonlinear Phenomena
    • Place of Presentation
      Yokohama, Japan
    • Year and Date
      2006-12-21
    • Related Report
      2008 Final Research Report

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Published: 2006-04-01   Modified: 2016-04-21  

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