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Mathematics of inverse problems and practical solution methods

Research Project

Project/Area Number 21340021
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section一般
Research Field General mathematics (including Probability theory/Statistical mathematics)
Research InstitutionThe University of Tokyo

Principal Investigator

YAMAMOTO Masahiro  東京大学, 大学院・数理科学研究科, 教授 (50182647)

Co-Investigator(Kenkyū-buntansha) ASHINO Ryuichi  大阪教育大学, 教育学部, 教授 (80249490)
ISO Yuusuke  京都大学, 大学院・情報学研究科, 教授 (70203065)
OHE Takashi  岡山理科大学, 理学部, 准教授 (90258210)
ONISHI Kazuei  茨城大学, 理学部, 元教授 (20078554)
TANUMA Kazumi  群馬大学, 工学部, 准教授 (60217156)
KUBO Shiro  大阪大学, 工学研究科, 元教授 (20107139)
WATANABE Michiyuki  新潟大学, 教育学部, 准教授 (90374181)
TRUSHIN Igor  東北大学, 学内共同利用施設等, 准教授 (80600337)
Co-Investigator(Renkei-kenkyūsha) NAKAGAWA Junichi  新日本製鐵・住金, 主幹研究員 (60373776)
Project Period (FY) 2009 – 2012
Project Status Completed (Fiscal Year 2012)
Budget Amount *help
¥16,900,000 (Direct Cost: ¥13,000,000、Indirect Cost: ¥3,900,000)
Fiscal Year 2012: ¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2011: ¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2010: ¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2009: ¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Keywords逆問題 / 数値解析 / 実用解法 / 正則化 / 安定化
Research Abstract

We made mathematical researches for various applied inverse problems and established numerical methods which are applicable practically. As applied inverse problems, we studied inverse coefficient problems, inverse source problems, inverse obstacle scattering problem and image reconstruction, and our mathematical subjects are the uniqueness and the stability.

Report

(5 results)
  • 2012 Annual Research Report   Final Research Report ( PDF )
  • 2011 Annual Research Report
  • 2010 Annual Research Report
  • 2009 Annual Research Report
  • Research Products

    (45 results)

All 2012 2011 2010 2009 Other

All Journal Article (31 results) (of which Peer Reviewed: 31 results) Presentation (11 results) (of which Invited: 2 results) Patent(Industrial Property Rights) (3 results)

  • [Journal Article] Partial Cauchy data for general second order elliptic operators in two dimensions2012

    • Author(s)
      O. Imanuvilov, G. Uhlmann and M. Yamamoto
    • Journal Title

      Publ. Res. Inst. Math. Sci

      Volume: 48 Pages: 971-1055

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Growth rate modeling and identification in the crystallization of polymers2012

    • Author(s)
      Y. Liu, X. Xu and M. Yamamoto
    • Journal Title

      Inverse Problems

      Volume: 28 Pages: 095008-13

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Conditional stability in determining a zeroth order coefficient in a half-order fractionaldiffusion equation by a Carleman estimate2012

    • Author(s)
      M. Yamamoto and Y. Zhang
    • Journal Title

      Inverse Problems

      Volume: 28 Pages: 105010-10

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Identification of two coefficients with data of one component for a nonlinear parabolic system2012

    • Author(s)
      M. Cristofol, P. Gaitan, H. Ramoul and M. Yamamoto
    • Journal Title

      Appl. Anal

      Volume: 91 Pages: 2073-2081

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Inverse boundary value problem for Schr¨odinger equation in two dimensions2012

    • Author(s)
      O. Imanuvilov and M. Yamamoto
    • Journal Title

      SIAM J. Math. Anal

      Volume: 44 Pages: 1333-1339

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Inverse problem by Cauchy data on anarbitrary sub-boundary for systems of elliptic equations2012

    • Author(s)
      O. Imanuvilov and M. Yamamoto
    • Journal Title

      Inverse Problems

      Volume: 28 Pages: 095015-30

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Unique continuation and approximate controllability for a degenerate parabolic equation2012

    • Author(s)
      P. Cannarsa, J. Tort and M. Yamamoto
    • Journal Title

      Appl. Anal

      Volume: 91 Pages: 1409-1425

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Reconstruction of the Stefan-Boltzmann coefficients in a heat-transfer process2012

    • Author(s)
      J. Cheng, S. Lu and M. Yamamoto
    • Journal Title

      Inverse Problems

      Volume: 28 Pages: 045007-17

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Partial Cauchy data for general second order elliptic operators in two dimensions2012

    • Author(s)
      O. Imanuvilov
    • Journal Title

      Publ. RIMS

      Volume: 48 Pages: 971-1055

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Determination of an electromagnetic potential for the Dirac equation2012

    • Author(s)
      A. Kawamoto
    • Journal Title

      Inverse Problems

      Volume: 28

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Identification of two coefficients with data of one component for a nonlinear parabolic system2012

    • Author(s)
      M. Cristofol
    • Journal Title

      Applicable Analysis

      Volume: 91 Pages: 2073-2081

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Inverse boundary value problem for Schr\"odinger equation in two dimensions2012

    • Author(s)
      O. Imanuvilov
    • Journal Title

      SIAM Math. Anal.

      Volume: 44 Pages: 1333-1339

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Kohzaburo Real-timereconstruction of time-varying point sources in a three-dimensional scalar wave equation2011

    • Author(s)
      Ohe, Takashi; Inui, Hirokazu; Ohnaka
    • Journal Title

      Inverse Problems

      Volume: 27, no. 11 Pages: 115011-19

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Kazumi Recovering conductivity at the boundary in three-dimensional electrical impedance tomography2011

    • Author(s)
      Nakamura, Gen; Ronkanen, Paivi; Siltanen, Samuli; Tanuma
    • Journal Title

      Inverse Probl. Imaging 5

      Volume: no. 2 Pages: 485-510

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Inverse boundary value problem by measuring Dirichlet data and Neumann data on disjoint sets2011

    • Author(s)
      O.Imanuvilov, G.Uhlamnn, M.Yamamoto
    • Journal Title

      Inverse Problems

      Volume: 27 Pages: 0850027-26

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Determination of second-order elliptic operators in two dimensions from partial Cauchy data2011

    • Author(s)
      O.Imanuvilov, G.Uhlamnn, M.Yamamoto
    • Journal Title

      Proc.Natl.Acad.Sci.USA

      Volume: 108 Pages: 467-472

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Initial value/boundary value problems for fractional diffusion-wave equations and applications to some inverse problems2011

    • Author(s)
      K.Sakamoto, M.Yamamoto
    • Journal Title

      J.Math.Anal.Appl.

      Volume: 382 Pages: 426-447

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] The Calder on problem with partial data in two dimensions2010

    • Author(s)
      O.Y. Imanuvilov, G. Uhlmann and M. Yamamoto
    • Journal Title

      J. Amer. Math. Soc

      Volume: 23 Pages: 655-691

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Remi Windowed Fourier transform of two-dimensional quaternionic signals2010

    • Author(s)
      Hitzer, Eckhard S. M.; Ashino, Ryuichi; Vaillancourt
    • Journal Title

      Appl. Math. Comput

      Volume: 216, no. 8 Pages: 2366-2379

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] A backwardproblem for the time-fractional diffusion equation2010

    • Author(s)
      J.J. Liu and M. Yamamoto
    • Journal Title

      Appl. Anal

      Volume: 89 Pages: 1769-1788

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] On the interplay of source conditions and variational inequalities for nonlinear ill-posed problems2010

    • Author(s)
      B. Hofmann and M. Yamamoto
    • Journal Title

      Appl. Anal

      Volume: 89 Pages: 1705-1727

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Determination of source terms in a degenerate parabolic equation2010

    • Author(s)
      P. Cannarsa, J. Tort and M.Yamamoto
    • Journal Title

      Inverse Problems

      Volume: 26 Pages: 105003-20

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] The Calder' on problem with partial data in two dimensions2010

    • Author(s)
      IMANUVILOV, Oleg, UHLMANN, Gunther, YAMAMOTO, Masahiro
    • Journal Title

      J.Amer.Math.Soc.

      Volume: 23 Pages: 655-691

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] The monotone Robin-Robin domain decomposition methods for the elliptic problems with Stefan-Boltzmann conditions2010

    • Author(s)
      CHEN, W., CHENG, J., YAMAMOTO, M., ZHANG, W.
    • Journal Title

      Comm.Comput.Physics

      Volume: 8 Pages: 642-662

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A numerical method for solving the inverse heat conduction problem without initial value2010

    • Author(s)
      WANG, Y., CHENG, J., NAKAGAWA, J., YAMAMOTO, Masahiro
    • Journal Title

      Inverse Problems in Sci.Eng.

      Volume: 18 Pages: 655-671

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Carleman estimates for parabolic equations and applications2009

    • Author(s)
      M. Yamamoto
    • Journal Title

      Inverse Problems

      Volume: 25

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Barbara On the identificationof a coefficient function in a nonlinear wave equation2009

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

      Inverse Problems

      Volume: 25 , no. 3 Pages: 035007-16

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] Carleman estimates for parabolic equations and applications2009

    • Author(s)
      YAMAMOTO, Masahiro
    • Journal Title

      Inverse Problems 25

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Uniqueness in an inverse problem for a one-dimensional fractional diffusion equation2009

    • Author(s)
      CHENG, Jin, NAKAGAWA, Junichi YAMAMOTO, Masahiro, YAMAZAKI, Tomohiro
    • Journal Title

      Inverse Problems 25

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On the evaluation of dilatometer experiments2009

    • Author(s)
      HOEMBERG, Dietmar, TOGOBYTSKA, Natalie, YAMAMOTO, Masahiro
    • Journal Title

      Applicable Analysis 88

      Pages: 669-681

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Carleman estimate with second large parameter for second order hyperbolic operators in a Riemannian manifold and applications in thermoelasticity

    • Author(s)
      M. Bellassoued and M. Yamamoto
    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Presentation] Coefficient inverse problem for transport equation2011

    • Author(s)
      M.Yamamoto
    • Organizer
      Chemnitz Symposium on Inverse Problems 2011
    • Place of Presentation
      ケムニッツ工科大学、ドイツ(招待講演)
    • Year and Date
      2011-09-28
    • Related Report
      2011 Annual Research Report
  • [Presentation] Uniqueness for 2D inverse boundary value problems for second-order elliptic equations by partial data2010

    • Organizer
      Interbational Conferenceon Inverse Problems
    • Place of Presentation
      Wuhan University, Wuhan, 中国
    • Year and Date
      2010-04-29
    • Related Report
      2012 Final Research Report
  • [Presentation] Uniqueness for 2D inverse boundary value problems for second-order elliptic eauations by Partial data2010

    • Author(s)
      YAMAMOTO, Masahiro
    • Organizer
      International Conference on Inverse Problems
    • Place of Presentation
      Wuhan University, Wuhan,中国
    • Year and Date
      2010-04-29
    • Related Report
      2010 Annual Research Report
  • [Presentation] 産業数学の実践:数学が解く産業現場 の問題:産学連携の経験を踏まえて2009

    • Organizer
      2009 年度公開講座『解析学の広がり』
    • Place of Presentation
      東京大学大学院数理科学研究科
    • Year and Date
      2009-10-24
    • Related Report
      2012 Final Research Report
  • [Presentation] Initial value/boundary value problems for fractional diffusion-waveequations and inverse problems2009

    • Organizer
      Workshop on Advances and Trends in Integral Equations
    • Place of Presentation
      Wasserschloss Klaffenbach (by Chemnitz), ドイツ
    • Year and Date
      2009-10-06
    • Related Report
      2012 Final Research Report
  • [Presentation] Practice of industrial mathematics related with the steel manufacturingprocess2009

    • Organizer
      The 7th International ISAAC Congress
    • Place of Presentation
      Imperial College of London, イギリス
    • Year and Date
      2009-07-16
    • Related Report
      2012 Final Research Report
  • [Presentation] Practice of industrial mathematics related with the steel manufacturing process2009

    • Author(s)
      YAMAMOTO, Masahiro
    • Organizer
      The 7th International ISAAC Congress
    • Place of Presentation
      Imperial College of London
    • Year and Date
      2009-07-16
    • Related Report
      2009 Annual Research Report
  • [Presentation] Inverse problems for diffusion equations of fractional orders2009

    • Organizer
      Chemnitz- RICAM Symposium on Inverse Problems
    • Place of Presentation
      Johann Radon Institute for Computational and Applied Mathematics (RICAM) Austrian Academy of Sciences, Linz, オーストリア
    • Year and Date
      2009-07-15
    • Related Report
      2012 Final Research Report
  • [Presentation] Inverse hyperbolic problem by a finitetime of observations with arbitrary initial values2009

    • Organizer
      International Conference on Mathematical Control Theory
    • Place of Presentation
      Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 中国
    • Year and Date
      2009-05-17
    • Related Report
      2012 Final Research Report
  • [Presentation] Uniqueness results by partial Cauchy data for 2-dimensional elliptic systems

    • Author(s)
      M. Yamamoto
    • Organizer
      Inverse and Ill-posed Problems in Math. Physics
    • Place of Presentation
      Novosibirsk, Russia
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] 逆問題が開く数学と産業の連携

    • Author(s)
      山本昌宏
    • Organizer
      サイバネットシステムシンポジウム
    • Place of Presentation
      東京
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Patent(Industrial Property Rights)]2010

    • Filing Date
      2010-05-13
    • Related Report
      2012 Final Research Report
  • [Patent(Industrial Property Rights)]2010

    • Filing Date
      2010-05-26
    • Related Report
      2012 Final Research Report
  • [Patent(Industrial Property Rights)]2009

    • Filing Date
      2009-07-01
    • Related Report
      2012 Final Research Report

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Published: 2009-04-01   Modified: 2019-07-29  

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