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Reconstruction schemes for inverse problems identifying unknown oefficients and boundaries for partial differential equations

Research Project

Project/Area Number 19340028
Research Category

Grant-in-Aid for Scientific Research (B)

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

Principal Investigator

NAKAMURA Gen  Hokkaido University, 大学院・理学研究院, 教授 (50118535)

Co-Investigator(Kenkyū-buntansha) HONDA Naofumi  北海道大学, 大学院・理学研究院, 准教授 (00238817)
TONEGAWA Yoshihiro  北海道大学, 大学院・理学研究院, 教授 (80296748)
TAIRA Kazuaki  筑波大学, 数理物質科学研究科, 教授 (90016163)
ISOZAKI Hiroshi  筑波大学, 数理物質科学研究科, 教授 (90111913)
YAMAMOTO Masahiro  東京大学, 大学院・数理科学研究所, 教授 (50182647)
SHIROTA Kenji  愛知県立大学, 情報科学部, 准教授 (90302322)
WATANABE Michiyuki  新潟大学, 教育学部, 准教授 (90374181)
OHE Takashi  岡山理科大学, 理学部, 准教授 (90258210)
TAKUWA Hideki  同志社大学, 理工学部, 准教授 (80403111)
Project Period (FY) 2007 – 2009
Project Status Completed (Fiscal Year 2009)
Budget Amount *help
¥18,850,000 (Direct Cost: ¥14,500,000、Indirect Cost: ¥4,350,000)
Fiscal Year 2009: ¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2008: ¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000)
Fiscal Year 2007: ¥9,750,000 (Direct Cost: ¥7,500,000、Indirect Cost: ¥2,250,000)
Keywords逆問題 / 散乱 / thermography / 流体方程式 / 非破壊検査法 / サーモグラフィー / dynamical probe method / Neumann-Diriclet map / 不連続係数熱作用素 / 基本解の勾配微分評価 / 熱伝導体 / 介在物 / 基本解 / 熱作用素 / 散乱の逆問題 / 境界値逆問題 / 熱伝導方程式 / nc respcnse test / probe methcd
Research Abstract

For 1) inverse scattering problems, 2) thermography, 3) inverse problems for equations in fluids, some new reconstruction schemes and an framework which integrates several known reconstruction schemes are given.

Report

(4 results)
  • 2009 Annual Research Report   Final Research Report ( PDF )
  • 2008 Annual Research Report
  • 2007 Annual Research Report
  • Research Products

    (61 results)

All 2010 2009 2008 2007

All Journal Article (38 results) (of which Peer Reviewed: 15 results) Presentation (23 results)

  • [Journal Article] Conditional stability for the hexagonal anisotropic elastic dynamical systems2009

    • Author(s)
      Lin, Ching-Lung, Nakamura, Gen.
    • Journal Title

      Comm. Partial Differential Equations 34, no. 10-12

      Pages: 1251-1264

    • Related Report
      2009 Final Research Report
  • [Journal Article] Well-posedness of an inverse problem of Navier-Stokes equations with the final overdetermination2009

    • Author(s)
      Fan, Jishan, Nakamura, Gen.
    • Journal Title

      J. Inverse Ill-Posed Probl. 17, no. 6

      Pages: 565-584

    • Related Report
      2009 Final Research Report
  • [Journal Article] Size estimates in thermog raphy2009

    • Author(s)
      Lei, Yi, Di Cristo, Michele., Nakamura, Gen.
    • Journal Title

      Appl.Anal. 88, no. 6

      Pages: 831-846

    • Related Report
      2009 Final Research Report
  • [Journal Article] Inverse problems for the Boussinesq system2009

    • Author(s)
      Fan, Jishan, Jiang, Yu, Nakamura, Gen
    • Journal Title

      Inverse Problems 25, no. 8

      Pages: 085007-10

    • Related Report
      2009 Final Research Report
  • [Journal Article] Numerical implementations of dynamical probe method for non-stationary heat equation2009

    • Author(s)
      Daido, Yuki, Lei, Yi, Liu, Jijun, Nakamura, Gen.
    • Journal Title

      Appl. Math. Comput. 211, no. 2

      Pages: 510-521

    • Related Report
      2009 Final Research Report
  • [Journal Article] Recovery of multiple obstacles by probe method2009

    • Author(s)
      Cheng, Jin, Liu, Jijun, Nakamura, Gen, Wang, Shengzhang
    • Journal Title

      Quart. Appl. Math. 67, no. 2

      Pages: 221-247

    • Related Report
      2009 Final Research Report
  • [Journal Article] On the identification of a coefficient function in a nonlinear wave equation2009

    • Author(s)
      Nakamura, Gen, Watanabe, Michiyuki, Kaltenbacher, Barbara
    • Journal Title

      Inverse Problems 25, no. 3

      Pages: 035007-16

    • Related Report
      2009 Final Research Report
  • [Journal Article] Size estimates in thermography2009

    • Author(s)
      Y.Lei ; M.Di Cristo ; G.Nakamura
    • Journal Title

      Appl.Anal. 88

      Pages: 831-846

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Numerical implementations of dynamical probe method for nonstationary heat equation2009

    • Author(s)
      Y.Daido ; Y.Lei ; J.Liu ; G.Nakamura
    • Journal Title

      Appl.Math. Comput. 211

      Pages: 510-521

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Conditional stability for the hexagonal anisotropic elastic dynamical systems.2009

    • Author(s)
      C-L.Lin ; G.Nakamura
    • Journal Title

      Comm.Partial Differential Equations 34

      Pages: 1251-1264

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Well-posedness of an inverse problem of Navier-Stokes equations with the final overdetermination2009

    • Author(s)
      J.Fan ; G.Nakamura
    • Journal Title

      J.Inverse III-Poed Probl. 17

      Pages: 565-584

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Recovery of multiple obstacles by probe method2009

    • Author(s)
      J.Cheng ; J.Liu ; G.Nakamura ; S.Wang
    • Journal Title

      Quart. Appl.Math. 67

      Pages: 221-247

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On the identification of a coefficient function in a nonlinear wave equation2009

    • Author(s)
      G.Nakamura ; M.Watanabe ; B.Kaltenbacher
    • Journal Title

      Inverse Problems 25

      Pages: 16-16

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Inverse problems for the Boussinesq system2009

    • Author(s)
      J.Fan ; Y.Jiang ; G.Nakamura
    • Journal Title

      Inverse Problems 25

      Pages: 10-10

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Local solvability of an inverse problem to the density-dependent Navier-Stokes equations2008

    • Author(s)
      Fan, Jishan, Nakamura, Gen
    • Journal Title

      Appl. Anal. 87, no. 10-11

      Pages: 1255-1265

    • Related Report
      2009 Final Research Report
  • [Journal Article] Unique continuation for the elastic transversely isotropic dynamical systems and its application2008

    • Author(s)
      Lin, Ching-Lung, Nakamura, Gen, Sini, Mourad
    • Journal Title

      J. Differential Equations 245, no. 10

      Pages: 3008-3024

    • Related Report
      2009 Final Research Report
  • [Journal Article] Inversion analysis for magnetic resonance elastography2008

    • Author(s)
      Nakamura, Gen, Jiang, Yu, Nagayasu, Sei, Cheng, Jin
    • Journal Title

      Appl. Anal. 87, no. 2

      Pages: 165-179

    • Related Report
      2009 Final Research Report
  • [Journal Article] Numerical differentiation for the second order derivatives of functions of two variables2008

    • Author(s)
      Nakamura, Gen, Wang, Shengzhang, Wang, Yanbo
    • Journal Title

      J. Comput. Appl. Math. 212, no. 2

      Pages: 341-358

    • Related Report
      2009 Final Research Report
  • [Journal Article] An inverse boundary value problem for a nonlinear wave equation2008

    • Author(s)
      Nakamura, Gen, Watanabe, Michiyuki
    • Journal Title

      Inverse Probl. Imaging 2, no. 1

      Pages: 121-131

    • Related Report
      2009 Final Research Report
  • [Journal Article] The noresponse approach and its relation to non-iterative methods for the inverse scattering2008

    • Author(s)
      Honda, Naofumi, Potthast, Roland, Nakamura, Gen, Sini, Mourad
    • Journal Title

      Ann. Mat. Pura Appl. (4)187, no. 1

      Pages: 7-37

    • NAID

      120006459458

    • Related Report
      2009 Final Research Report
  • [Journal Article] Unique continuation for the elastic transversely isotropic dynamical systems and its application2008

    • Author(s)
      Lin, Ching-Lung
    • Journal Title

      Journal of Differential Equations 245

      Pages: 3008-3024

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Inversion analysis for magnetic resonance elastography2008

    • Author(s)
      Nakamura, Gen
    • Journal Title

      Applicable Analysis 87

      Pages: 165-179

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Numerical differentiation for the second order derivatives of functions of two variables2008

    • Author(s)
      Nakamura, Gen
    • Journal Title

      Journal of Computational and Applied Mathematics 212

      Pages: 341-358

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] An inverse boundary value problem for a nonlinear waveequation2008

    • Author(s)
      Nakamura, Gen
    • Journal Title

      Inverse Problems and Imaging 2

      Pages: 121-131

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] The no-response approach and its relation to non-iterative methods for the inverse scattering2008

    • Author(s)
      Honda, Naofumi
    • Journal Title

      Annali di Matematica Pura ed Applicata 187

      Pages: 7-37

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Identification of a non-convex obstacle for acoustical scattering2007

    • Author(s)
      Nakamura, Gen, Yoshida, Kazuki
    • Journal Title

      J. Inverse Ill-Posed Probl. 15, no. 6

      Pages: 611-624

    • Related Report
      2009 Final Research Report
  • [Journal Article] Mathematical and physical interpretation of the solution to the initial-boundary value problem in linear hyperbolic thermoelasticity theory2007

    • Author(s)
      Gawinecki, Jerzy August, Sikorska, Beata, Nakamura, Gen, Rafa, Jozef.
    • Journal Title

      ZAMM Z. Angew. Math. Mech. 87, no. 10

      Pages: 715-746

    • Related Report
      2009 Final Research Report
  • [Journal Article] Obstacle and boundary determination from scattering data2007

    • Author(s)
      Nakamura, Gen, Sini, Mourad
    • Journal Title

      SIAM J. Math. Anal. 39, no. 3

      Pages: 819-837

    • Related Report
      2009 Final Research Report
  • [Journal Article] A probe method for the inverse boundary value problem of nonstationary heat equations2007

    • Author(s)
      Daido, Yuki, Kang, Hyeonbae, Nakamura, Gen
    • Journal Title

      Inverse Problems 23, no. 5

      Pages: 1787-1800

    • Related Report
      2009 Final Research Report
  • [Journal Article] Variational approach for identifying a coefficient of the wave equation2007

    • Author(s)
      Choi, Cheok, Nakamura, Gen, Shirota, Kenji
    • Journal Title

      Cubo 9, no. 2

      Pages: 81-101

    • NAID

      120006459457

    • Related Report
      2009 Final Research Report
  • [Journal Article] A variational approach for an inverse dynamical problem for composite beams2007

    • Author(s)
      Morassi, Antonio, Nakamura, Gen, Shirota, Kenji, Sini, Mourad
    • Journal Title

      European J. Appl. Math. 18, no. 1

      Pages: 21-55

    • Related Report
      2009 Final Research Report
  • [Journal Article] Reconstruction of the shape and surface impedance from acoustic scattering data for an arbitrary cylinder2007

    • Author(s)
      Liu, Jijun., Nakamura, Gen, Sini, Mourad
    • Journal Title

      SIAM J. Appl. Math. 67, no. 4

      Pages: 1124-1146

    • Related Report
      2009 Final Research Report
  • [Journal Article] A new approach and error analysis for reconstructing the scattered wave by the point source method2007

    • Author(s)
      Liu, Jijun, Nakamura, Gen, Potthast, Roland
    • Journal Title

      J. Comput. Math. 25, no. 2

      Pages: 113-130

    • Related Report
      2009 Final Research Report
  • [Journal Article] Vanishing shear viscosity limit in the magnetohydrodynamic equations2007

    • Author(s)
      Fan, Jishan, Jiang, Song, Nakamura, Gen
    • Journal Title

      Comm. Math. Phys. 270, no. 3

      Pages: 691-708

    • Related Report
      2009 Final Research Report
  • [Journal Article] Three spheres inequalities for a two-dimensional ellipticsystem and its application2007

    • Author(s)
      Lin, Ching-Lung, Nakamura, Gen, Wang, Jenn-Nan
    • Journal Title

      J. Differential Equations 232, no. 1

      Pages: 329-351

    • Related Report
      2009 Final Research Report
  • [Journal Article] Identification of a non-conex dostacle for acusticl scuttering2007

    • Author(s)
      Gen Nakamura
    • Journal Title

      J. Inverse Ill-Posed Probl. 15

      Pages: 611-624

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Obstacle and boundary determination from scattering data2007

    • Author(s)
      Gen Nateamura
    • Journal Title

      SIAM J. Math. Anol. 39

      Pages: 819-837

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Three sphese inequalitieo for a two-dimensional elliptic sgstemo and its appl.2007

    • Author(s)
      Gen Nakamura
    • Journal Title

      J. Differential Equations 232

      Pages: 329-351

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Presentation] 生体粘弾性に関するデータ解析2010

    • Author(s)
      江渝, 中村玄
    • Organizer
      日本応用数理学会 2010年研究部会連合発表会
    • Place of Presentation
      筑波大学
    • Year and Date
      2010-03-08
    • Related Report
      2009 Final Research Report
  • [Presentation] 生体粘弾性に関するデータ解析2010

    • Author(s)
      江渝;中村玄
    • Organizer
      日本応用数理学会2010年研究部会連合発表会
    • Place of Presentation
      筑波大学
    • Year and Date
      2010-03-08
    • Related Report
      2009 Annual Research Report
  • [Presentation] Mathematical analysis for thermal non destructive testing2010

    • Author(s)
      中村玄
    • Organizer
      日本数学会年会
    • Place of Presentation
      慶應義塾大学矢上キャンパス
    • Related Report
      2009 Final Research Report
  • [Presentation] Analytic extension and reconstruction of obstacles for elliptic operators2010

    • Author(s)
      中村玄, 本多尚文, M. Sini
    • Organizer
      日本数学会年会
    • Place of Presentation
      慶應義塾大学矢上キャンパス
    • Related Report
      2009 Annual Research Report 2009 Final Research Report
  • [Presentation] MREによる生体弾性率測定法の数理2010

    • Author(s)
      中村玄
    • Organizer
      ワークショップ「変分法と領域摂動」
    • Place of Presentation
      神戸インスティチュート
    • Related Report
      2009 Annual Research Report 2009 Final Research Report
  • [Presentation] Mathematical analysis for thertmal non destructive testing2010

    • Author(s)
      中村玄
    • Organizer
      日本数学会年会
    • Place of Presentation
      慶應義塾大学矢上キャンパス
    • Related Report
      2009 Annual Research Report
  • [Presentation] Asymptotic Analysis for Magnetic Resonance Elastography2009

    • Author(s)
      Jiang, Yu, Nakamura, Gen, Fujiwara, Hiroshi
    • Organizer
      International conference on Inverse Problems and its Applications
    • Place of Presentation
      Hanbat National University, Daejeon, Korea
    • Year and Date
      2009-08-19
    • Related Report
      2009 Final Research Report
  • [Presentation] Asymptotic Analysis for Magnetic Resonance Elastography2009

    • Author(s)
      Y.Jiang ; H.Fujiwara ; G.Nakamura
    • Organizer
      Inverse Problems and its Applications
    • Place of Presentation
      Hanbat National Univ.,韓国
    • Year and Date
      2009-08-19
    • Related Report
      2009 Annual Research Report
  • [Presentation] Inverse Problems for Reconstructing the Medium Discontinuity2009

    • Author(s)
      Nakamura, Gen
    • Organizer
      Applied Inverse Problems
    • Place of Presentation
      Vienna
    • Year and Date
      2009-07-24
    • Related Report
      2009 Final Research Report
  • [Presentation] Inverse Problems for Reconstructing the Medium Discontinuity2009

    • Author(s)
      G.Nakamura
    • Organizer
      Applied Inverse Problems
    • Place of Presentation
      Vienna, Austria
    • Year and Date
      2009-07-24
    • Related Report
      2009 Annual Research Report
  • [Presentation] MRE に関する漸近解析2009

    • Author(s)
      江渝, 中村玄, 藤原宏志
    • Organizer
      第58回理論応用力学講演会
    • Place of Presentation
      日本学術会議
    • Year and Date
      2009-06-10
    • Related Report
      2009 Final Research Report
  • [Presentation] MREに関する漸近解析2009

    • Author(s)
      江渝、中村玄、藤原宏志
    • Organizer
      第58回理論応用力学講演会
    • Place of Presentation
      日本学術会議,東京都
    • Year and Date
      2009-06-10
    • Related Report
      2009 Annual Research Report
  • [Presentation] Inverse Problems for Reconstructing the Medium Discontinuity2009

    • Author(s)
      中村玄
    • Organizer
      数理科学セミナー
    • Place of Presentation
      大阪電気通信大学寝屋川キャンパス
    • Related Report
      2009 Annual Research Report 2009 Final Research Report
  • [Presentation] Analytic Extension and Reconstruction of Obstacles from Few Measurements for Elliptic Second Order Operators2009

    • Author(s)
      Honda, Naofumi, Nakamura, Gen, Mourad, Sini
    • Place of Presentation
      Univ. South Wales, Sydney
    • Related Report
      2009 Final Research Report
  • [Presentation] Asymptotic analysis for magnetic resonance elastography2009

    • Author(s)
      江渝, 中村玄, 藤原宏志
    • Organizer
      2009年日本数学会
    • Place of Presentation
      東京大学駒場キャンパス
    • Related Report
      2009 Final Research Report
  • [Presentation] Analytic Extension and Reconstruction of Obstacles from Few Measurements for Elliptic Second Order Operators2009

    • Author(s)
      N.Honda ; G.Nakamura ; M.Sini
    • Organizer
      Pacific Rim Conf.
    • Place of Presentation
      Univ.New South Wales, Australia
    • Related Report
      2009 Annual Research Report
  • [Presentation] Asymptotic analysis for magnetic resonance elastography2009

    • Author(s)
      江渝、中村玄、藤原宏志
    • Organizer
      日本数学会
    • Place of Presentation
      東京大学駒場キャンパス
    • Related Report
      2009 Annual Research Report
  • [Presentation] Reconstruction of an unknown inclusionby thermal imaging2008

    • Author(s)
      Isakov, Victor, Kim Kyoungsun, Nakamura, Gen.
    • Organizer
      Eccomas
    • Place of Presentation
      Venis
    • Year and Date
      2008-07-02
    • Related Report
      2009 Final Research Report
  • [Presentation] On the identification of a coefficient function in a nonlinear wave equation2008

    • Author(s)
      渡辺道之, 中村玄, B. Kaltenbacher
    • Organizer
      日本数学会年会
    • Place of Presentation
      近畿大学
    • Related Report
      2009 Final Research Report
  • [Presentation] Reconstruction of an unknown inclusion by thermal imaging2008

    • Author(s)
      K. Kim, 中村玄, V. Isakov
    • Organizer
      日本数学会年会
    • Place of Presentation
      近畿大学
    • Related Report
      2009 Final Research Report
  • [Presentation] Identification of a non-convex obstacle for acoustical scattering2007

    • Author(s)
      中村玄, 吉田一樹
    • Organizer
      日本数学会秋季総合分科会
    • Place of Presentation
      東北大学
    • Related Report
      2009 Final Research Report
  • [Presentation] MREによる弾性係数と粘性係数の同定法の数理2007

    • Author(s)
      中村玄, 江渝, 永安聖, 程晋
    • Organizer
      日本数学会秋季総合分科会
    • Place of Presentation
      東北大学
    • Related Report
      2009 Final Research Report
  • [Presentation] 非凸形状音響散乱体の同定2007

    • Author(s)
      中村 玄
    • Organizer
      日本応用数理学会2007年度年会
    • Place of Presentation
      北海道大学
    • Related Report
      2007 Annual Research Report

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Published: 2007-04-01   Modified: 2016-04-21  

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