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Study of Inverse Problems for Family of Elasticity Equations

Research Project

Project/Area Number 22340023
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  北海道大学, 名誉教授 (50118535)

Co-Investigator(Kenkyū-buntansha) JIMBO Shuichi  北海道大学, 大学院・理学研究院, 教授 (80201565)
HONDA Naofumi  北海道大学, 大学院・理学研究院, 准教授 (00238817)
KAWSHITA Misio  広島大学, 大学院・理学研究科, 教授 (80214633)
TANUMA Kazumi  群馬大学, 大学院・工学研究科, 准教授 (60217156)
WATANABE Michiyuki  新潟大学, 人文社会・教育学系, 准教授 (90374181)
SHIROTA Kenji  愛知県立大学, 情報学部, 准教授 (90302322)
Project Period (FY) 2010 – 2012
Project Status Completed (Fiscal Year 2012)
Budget Amount *help
¥14,820,000 (Direct Cost: ¥11,400,000、Indirect Cost: ¥3,420,000)
Fiscal Year 2012: ¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000)
Fiscal Year 2011: ¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2010: ¥5,590,000 (Direct Cost: ¥4,300,000、Indirect Cost: ¥1,290,000)
Keywords応用解析 / 逆問題 / 粘弾性方程式 / MRE / 安定性 / 断層同定 / 弾性係数 / 粘性係数 / レーリー波 / 非線形波動方程式 / 粘弾性 / 光トモグラフィー / 解の構造
Research Abstract

Some studies were done and obtained sufficient results on the data analysis of elastography which measures the visco-elasticity of tissues in a living body non-invasively, and as their related studies, the LSM (linear sampling method) for parabolic equations and Carleman estimate for anomalous diffusion equations. We completed our recent year study on the dispersion formula of the speed of Rayleigh wave for half space depth dependent anisotrpic elastic media with residual stress. We gave an inversion scheme for detecting damage of connectors of steel-concrete composite beam.

Report

(4 results)
  • 2012 Annual Research Report   Final Research Report ( PDF )
  • 2011 Annual Research Report
  • 2010 Annual Research Report
  • Research Products

    (50 results)

All 2013 2012 2011 2010 Other

All Journal Article (25 results) (of which Peer Reviewed: 25 results) Presentation (24 results) Patent(Industrial Property Rights) (1 results) (of which Overseas: 1 results)

  • [Journal Article] Dispersion of Rayleigh Waves in Vertically-Inhomogeneous Prestressed Elastic Media2013

    • Author(s)
      Chi-Sing Man,Gen Nakamura,Kazumi Tanuma and Shengzhang Wang
    • Journal Title

      IMA Journal of Applied Mathematics

      Volume: (in press) Issue: 1 Pages: 1-38

    • DOI

      10.1093/imamat/hxt025

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Model Independent MRE Data Analysis2013

    • Author(s)
      Kogo Yoshikawa and Gen Nakamura
    • Journal Title

      Computational and Mathematical Methods in Medicine

      Volume: vol. 2013

    • URL

      http://dx.doi.org/10.1155/2013/912920

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Unique continuation property for the anomalous diffusion and its application2013

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

      Journal of Differential Equations,Online publication

      Volume: 254 Issue: 9 Pages: 3715-3728

    • DOI

      10.1016/j.jde.2013.01.039

    • Related Report
      2012 Annual Research Report 2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] A gradient estimate for solutions to parabolic equations with discontinuous coefficients2013

    • Author(s)
      Jishan Fan, Kyoungsun Kim, Sei Nagayasu and Gen Nakamura
    • Journal Title

      Electron. J. Diff. Equ.

      Volume: Vol.2013 Pages: 1-24

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] The Green function of the interior transmission problem and its applications2013

    • Author(s)
      K. Kim, G. Nakamura, M. Sini
    • Journal Title

      Inverse Problems and Imaging

      Volume: 6 Pages: 487-521

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Inverse boundary value problem for the heat equation with discontinuous coefficients2013

    • Author(s)
      G. Nakamura and S. Sasayama
    • Journal Title

      J. Inverse Ill-Posed Probl

      Volume: -

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Model Independent MRE Data Analysis2013

    • Author(s)
      K.Yoshikawa, G.Nakamura
    • Journal Title

      Computational and Mathematical Methods in Medicine

      Volume: vol. 2013 Pages: 1-11

    • DOI

      10.1155/2013/912920

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Local maxima of solutions to some nonsymmetric reaction-diffusion systems2013

    • Author(s)
      J. Nakagawa, G. Nakamura, S. Sasayama, H. Wang
    • Journal Title

      Mathematical Methods in The Applied Sciences

      Volume: -

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Linear sampling method for identifying cavities in a heat conductor.2012

    • Author(s)
      Horst Heck, Gen Nakamura and Haibing Wang
    • Journal Title

      Inverse Problems

      Volume: No.7 Pages: 75014-75014

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] The Green function of the interior transmission problem and its applications2012

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

      Inverse Problems andImaging

      Volume: 6 Pages: 487-521

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] A non-destructive method for damage Detection in steel-concrete Structures based on finite eigendata2012

    • Author(s)
      Shuichi Jimbo, Antonino Morassi, Gen Nakamura and Kenji Shirota
    • Journal Title

      Inverse Problems in Science and Engineering.

      Volume: 20 Pages: 233-270

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Inverse scattering for obliquely incident polarized electromagnetic waves2012

    • Author(s)
      G.Nakamura, H. Wang
    • Journal Title

      Inverse Problems

      Volume: 28 Issue: 1 Pages: 019502-019502

    • DOI

      10.1088/0266-5611/29/1/019502

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Direct electromagnetic scattering problem from an imperfectly conducting cylinder at oblique incidence2012

    • Author(s)
      G. Nakamura, H. Haibing
    • Journal Title

      J. Math. Anal. Appl.

      Volume: - Issue: 1 Pages: 142-155

    • DOI

      10.1016/j.jmaa.2012.07.049

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Linear sampling method for identifying cavities in a heat conductor2012

    • Author(s)
      H. Heck, G.Nakamura, H. Haibing
    • Journal Title

      Inverse Problems

      Volume: 28 Issue: 7 Pages: 075014-075014

    • DOI

      10.1088/0266-5611/28/7/075014

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] The integral equation method for electromagnetic scattering problem at oblique incidence2012

    • Author(s)
      H. Wang, G.Nakamura
    • Journal Title

      Applied Numerical Mathematics

      Volume: 62 Pages: 860-873

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On uniqueness of an inverse problem in electromagnetic obstacle scattering for an impedance cylinder2012

    • Author(s)
      G. Nakamura, B. Sleeman, H. Haibing
    • Journal Title

      Inverse Problems

      Volume: 28 Issue: 5 Pages: 055012-055012

    • DOI

      10.1088/0266-5611/28/5/055012

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A non-destructive method for damage detection in steel-concrete structures based on finite eigendata2012

    • Author(s)
      S.Jimbo, A.Morassi, G.Nakamura, K.Shirota
    • Journal Title

      Inverse Problems in Science and Engineering

      Volume: 20 Pages: 233-270

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Approximate steady state models for magnetic resonance elastography2011

    • Author(s)
      Yu, Jiang, Hiroshi Fujiwa
    • Journal Title

      SIAM Journal on Applied Mathematics

      Volume: 71 Pages: 1965-1989

    • Related Report
      2012 Final Research Report 2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Quantitative uniqueness for second order elliptic operators with strongly singular coefficients2011

    • Author(s)
      C-L Lin, G.Nakamura, J-N.Wang
    • Journal Title

      Rev.Mat.Iberoam

      Volume: 27 Pages: 475-491

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Reconstruction of an unknown inclusion by thermography.2010

    • Author(s)
      Victor Isakov, Kyoungsun Kim and Gen Nakamura
    • Journal Title

      Ann. Sc. Norm. Super. Pisa Cl. Sci.

      Volume: (5)9 Pages: 725-758

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Unique continuation property for a coupled second-fourth order dynamical system and its application.2010

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

      SIAM J. Math. Anal.

      Volume: 42 Pages: 2318-2336

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Unique continuation property for a coupled second-fourth order dynamical system and its application2010

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

      SIAM J. Math. Anal.

      Volume: 42 Pages: 2318-2336

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Optimal three-ball inequalities and quantitative uniqueness for the Lame system with Lipschitz coefficients2010

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

      Duke Math. J.

      Volume: 155 Pages: 189-204

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] The identification of a penetrable obstacle with mixed transmission conditions from far field measurements2010

    • Author(s)
      Cakoni, Fioralba; Nakamura, Gen; Sini, Mourad; Zeev, Noam
    • Journal Title

      Appl. Anal.

      Volume: 89 Pages: 67-86

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Inverse boundary value problem for the heat equation with discontinuous coeffcients, J.

    • Author(s)
      Gen Nakamura and Sasayama Satoshi
    • Journal Title

      Inverse Ill-Posed Probl.,accepted

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Presentation] Reconstructionscheme for diffusion equations2012

    • Author(s)
      Gen Nakamura
    • Organizer
      MSJ-KMS Joint Meeting
    • Place of Presentation
      Kyushu Univ.
    • Year and Date
      2012-09-17
    • Related Report
      2012 Final Research Report
  • [Presentation] MREデータの逆解析手法2012

    • Author(s)
      中村玄
    • Organizer
      第61回理論応用力学講演会
    • Place of Presentation
      東京大学生産技術研究所
    • Year and Date
      2012-03-09
    • Related Report
      2012 Final Research Report
  • [Presentation] MREデータの逆解析手法2012

    • Author(s)
      中村玄
    • Organizer
      第61回理論応用力学講演会
    • Place of Presentation
      東京大学生産技術研究所(東京都)(招待講演)
    • Year and Date
      2012-03-09
    • Related Report
      2011 Annual Research Report
  • [Presentation] Reconstruction schemes for diffusion equations, Inverse and Il-posed Problems of Mathematical Physics2012

    • Author(s)
      Gen Nakamura
    • Organizer
      Dedicated to the 80 th anniversary of the birthdayof Academician Mikhail Mikhailovich Lavrent'ev
    • Place of Presentation
      Novosibirsk.
    • Related Report
      2012 Final Research Report
  • [Presentation] Linear samplingmethod for 2nd order parabolic equations2012

    • Author(s)
      Gen Nakamura
    • Organizer
      Inverse Problems and PDE Control
    • Place of Presentation
      Sichuan Univ.
    • Related Report
      2012 Final Research Report
  • [Presentation] Magnetic resonanceelastography, data analysis2012

    • Author(s)
      Gen Nakamura
    • Organizer
      Waves and imaging in complex media
    • Place of Presentation
      FORTH, Crete
    • Related Report
      2012 Final Research Report
  • [Presentation] Stability estimate of stiffness from MRE data2012

    • Author(s)
      Gen Nakamura
    • Organizer
      Semi- classical and multiscale aspects of wave propaga-tion
    • Place of Presentation
      acmac, Crete.
    • Related Report
      2012 Final Research Report
  • [Presentation] Reconstruction scheme for active thermography2011

    • Author(s)
      Gen Nakamura
    • Place of Presentation
      Newton Institute, Cambridge.
    • Year and Date
      2011-09-20
    • Related Report
      2012 Final Research Report
  • [Presentation] Active thermo-graphy and dynamical probe method2011

    • Author(s)
      Gen Nakamura
    • Organizer
      Mini-Workshop: Nonlinear Least Squares in Shape Identification
    • Place of Presentation
      Oberwolfach, Germany.
    • Year and Date
      2011-01-18
    • Related Report
      2012 Final Research Report
  • [Presentation] Active Thermography and Dynamical Probe Method2011

    • Author(s)
      Gen Nakamura
    • Organizer
      Mini-Workshop : Nonlinear Least Squares in Shape Identification
    • Place of Presentation
      Oberwolfach, Germany 招待講演
    • Year and Date
      2011-01-18
    • Related Report
      2010 Annual Research Report
  • [Presentation] Dynamical probe method for anisotropic heat conductors2011

    • Author(s)
      Gen Nakamura
    • Organizer
      19th Workshop on Differential Equations and Its Applications
    • Place of Presentation
      Cheng-Kung Univ., Tainan, Taiwan
    • Year and Date
      2011-01-15
    • Related Report
      2012 Final Research Report
  • [Presentation] Dynamical probe method for anisotropic heat conductors, 19th Workshop on Differential Equations and Its Applications2011

    • Author(s)
      Gen Nakamura
    • Organizer
      19th Workshop on Differential Equations and Its Applications (plenary talk)
    • Place of Presentation
      Cheng-Kung Univ., Tainan, Taiwan 招待講演
    • Year and Date
      2011-01-15
    • Related Report
      2010 Annual Research Report
  • [Presentation] Linear sampling method for heat conductors2011

    • Author(s)
      Gen Nakamura
    • Organizer
      Inverse Problems of PDEs and Related Topics
    • Place of Presentation
      RIMS, Kyoto Univ.
    • Related Report
      2012 Final Research Report
  • [Presentation] Reconstruction schemes for diffusion equations2011

    • Author(s)
      Gen Nakamura
    • Organizer
      Finnish-Japanese-Korean workshop on inverse problems
    • Place of Presentation
      Univ. of Helsinki.
    • Related Report
      2012 Final Research Report
  • [Presentation] Data analysis formicro-MRE measured data Bio- mechanical Imaging Mini-sympo- sium in Applied Inverse Problems Conference2011

    • Author(s)
      Gen Nakamura
    • Place of Presentation
      Univ. of Texas A&M.
    • Related Report
      2012 Final Research Report
  • [Presentation] Lectures on severalreconstruction schemes for inverseproblem2011

    • Author(s)
      Gen Nakamura
    • Organizer
      Madrid Special Trimester on Inverse Problems: Theoretical and Numerical Aspects of Inverse Problems and Scattering Theory
    • Place of Presentation
      ICMAT, Madrid.
    • Related Report
      2012 Final Research Report
  • [Presentation] Dynamical probemethod for anisotropic heat conductors2010

    • Author(s)
      Gen Nakamura
    • Organizer
      ICIP 2010
    • Place of Presentation
      Hong Kong City Univ., Hong Kong, China
    • Year and Date
      2010-12-15
    • Related Report
      2012 Final Research Report
  • [Presentation] Dynamical Probe Method for Anisotropic Heat Conductors2010

    • Author(s)
      Gen Nakamura
    • Organizer
      ICIP2010
    • Place of Presentation
      Hong Kong City Univ., Hong Kong, China 招待講演
    • Year and Date
      2010-12-15
    • Related Report
      2010 Annual Research Report
  • [Presentation] Gradient estimate ofsolutions of parabolic operator with discontinuous coefficients2010

    • Author(s)
      Gen Nakamura
    • Organizer
      Inverse Prob- lems Seminar
    • Place of Presentation
      MSRI, Berkeley, USA
    • Year and Date
      2010-09-29
    • Related Report
      2012 Final Research Report
  • [Presentation] Gradient Estimate of Solutions of Parabolic Operator with Discontinuous Coefficients2010

    • Author(s)
      Gen Nakamura
    • Organizer
      Inverse Prablems Seminar (invited talk)
    • Place of Presentation
      MSRI, Berkeley, USA 招待講演
    • Year and Date
      2010-09-29
    • Related Report
      2010 Annual Research Report
  • [Presentation] Inverse spectralproblem for identifying damage in steel-concrete composite beams2010

    • Author(s)
      Gen Nakamura
    • Organizer
      日本土木学会、第13回応用力学シンポジウ ム
    • Place of Presentation
      北海道大学
    • Year and Date
      2010-08-31
    • Related Report
      2012 Final Research Report
  • [Presentation] Inverse Spectral Problem for Identifying Damage in Steel-Concrete Composite Beams2010

    • Author(s)
      中村玄
    • Organizer
      日本土木学会、第13回応用力学シンポジウム(基調講演)
    • Place of Presentation
      北海道大学 招待講演
    • Year and Date
      2010-08-31
    • Related Report
      2010 Annual Research Report
  • [Presentation] Time resolved diffu- sive optical tomography, Workshop on Optical Tomography2010

    • Author(s)
      Gen Nakamura
    • Organizer
      Workshop on Optical Tomography
    • Place of Presentation
      BIRS, Banff, Canada
    • Related Report
      2012 Final Research Report
  • [Presentation] Time Resolved Diffusive Optical Tomography, Workshop on Optical Tomography2010

    • Author(s)
      Gen Nakamura
    • Organizer
      Workshop on Optical Tomography (invited talk)
    • Place of Presentation
      BIRS, Banff, Canada 招待講演
    • Related Report
      2010 Annual Research Report
  • [Patent(Industrial Property Rights)] MRE用の加振装置、加振システム、おおよび加振方法2011

    • Inventor(s)
      但野茂、梶原逸郎、藤崎和弘、高尾 聖心、中村玄、Jiang Yu,菅幹生
    • Industrial Property Rights Holder
      北海道大学、千葉大学
    • Filing Date
      2011-08-25
    • Related Report
      2012 Final Research Report
    • Overseas

URL: 

Published: 2010-08-23   Modified: 2019-07-29  

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