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New development of the enclosure method for inverse obstacle scattering

Research Project

Project/Area Number 25400155
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Mathematical analysis
Research InstitutionHiroshima University

Principal Investigator

Ikehata Masaru  広島大学, 工学研究院, 教授 (90202910)

Co-Investigator(Renkei-kenkyūsha) ITOU HIROMICHI  東京理科大学, 理学部, 講師 (30400790)
Project Period (FY) 2013-04-01 – 2017-03-31
Project Status Completed (Fiscal Year 2016)
Budget Amount *help
¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000)
Fiscal Year 2016: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2015: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2013: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
KeywordsInverse problems / enclosure method / inverse scattering / wave equation / Maxwell system / 囲い込み法 / 偏微分方程式に対する逆問題 / 波動方程式 / 有限時間観測 / 非破壊検査 / 物体散乱逆問題 / inverse problems / non destructive testing / obstacle scattering / inverse problem / bistatic data / Robin condition / acoustic wave
Outline of Final Research Achievements

First, inverse obstacle scattering problems of waves governed by the classical wave equation and Maxwell system under several boundary conditions have been considered by using the enclosure method in the finite time domain. Several formulas for extracting information about the location, shape and further the quantitative and qualitative state of the surface of the obstacle from the observed wave are given. Second, a new version of the time domain enclosure method using a single input has been discovered.
Third, a method letting us know the estimation of the location together with the existence/nonexistence of unknown discontinuity embedded in a rough background medium from the observed wave has been introduced.

Report

(5 results)
  • 2016 Annual Research Report   Final Research Report ( PDF )
  • 2015 Research-status Report
  • 2014 Research-status Report
  • 2013 Research-status Report
  • Research Products

    (33 results)

All 2017 2016 2015 2014 2013 Other

All Journal Article (11 results) (of which Int'l Joint Research: 1 results,  Peer Reviewed: 11 results,  Open Access: 2 results,  Acknowledgement Compliant: 7 results) Presentation (18 results) (of which Int'l Joint Research: 5 results,  Invited: 14 results) Remarks (4 results)

  • [Journal Article] On finding an obstacle with the Leontovich boundary condition via the time domain enclosure method2017

    • Author(s)
      Masaru Ikehata
    • Journal Title

      Inverse Problems and Imaging

      Volume: 11 Issue: 1 Pages: 99-123

    • DOI

      10.3934/ipi.2017006

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] A remark on finding the coefficient of the dissipative boundary condition via the enclosure method in the time domain2017

    • Author(s)
      Masaru Ikehata
    • Journal Title

      Math. Mech. Appl. Sci.

      Volume: 40 Issue: 4 Pages: 915-927

    • DOI

      10.1002/mma.4021

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed
  • [Journal Article] The enclosure method for inverse obstacle scattering over a finite time interval: IV. Extraction from a single point on the graph of the response operator2017

    • Author(s)
      Masaru Ikehata
    • Journal Title

      Journal of Inverse and Ill-Posed Problems

      Volume: 印刷中 Issue: 6 Pages: 747-761

    • DOI

      10.1515/jiip-2016-0023

    • Related Report
      2016 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] The enclosure method for inverse obstacle scattering using a single electromagnetic wave in time domain2016

    • Author(s)
      Masaru Ikehata
    • Journal Title

      Inverse Problems and Imaging

      Volume: 10 Issue: 1 Pages: 131-163

    • DOI

      10.3934/ipi.2016.10.131

    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] Trusted frequency region of convergence for the enclosure method in thermal imaging2016

    • Author(s)
      Masaru Ikehata, Kiwoon Kwon
    • Journal Title

      Journal of Inverse and Ill-Posed Problems

      Volume: 印刷中 Issue: 1 Pages: 81-97

    • DOI

      10.1515/jiip-2016-0001

    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] The enclosure method for an inverse problem arising from a spot welding2015

    • Author(s)
      Masaru Ikehata, Hiromichi Itou, Akira Sasamoto
    • Journal Title

      Math. Mech. Appl. Sci.

      Volume: 印刷中 Issue: 13 Pages: 3565-3575

    • DOI

      10.1002/mma.3799

    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] On finding an obstacle embedded in the rough background medium via the enclosure method in the time domain2015

    • Author(s)
      Masaru Ikehata
    • Journal Title

      Inverse Problems

      Volume: 31 Issue: 8 Pages: 085011-085011

    • DOI

      10.1088/0266-5611/31/8/085011

    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] An inverse problem for a three-dimensional heat equation in thermal imaging and the enclosure method2014

    • Author(s)
      Ikehata, M. and Kawashita, M.
    • Journal Title

      Inverse Problems and Imaging

      Volume: 8 Issue: 4 Pages: 1073-1116

    • DOI

      10.3934/ipi.2014.8.1073

    • Related Report
      2014 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Estimates of the integral kernels arising from inverse problems for a three-dimensional heat equation in thermal imging2014

    • Author(s)
      Ikehata, M. and Kawashita, M.
    • Journal Title

      Kyoto J. Math.

      Volume: 54 Issue: 1 Pages: 1-50

    • DOI

      10.1215/21562261-2400265

    • Related Report
      2014 Research-status Report
    • Peer Reviewed
  • [Journal Article] Extracting the geometry of an obstacle and a zeroth-order coefficient of a boundary condition via the enclosure method using a single reflected wave over a finite time interval2014

    • Author(s)
      Ikehata,M.
    • Journal Title

      Inverse Problems

      Volume: 30 Issue: 4 Pages: 045011-045011

    • DOI

      10.1088/0266-5611/30/4/045011

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] The enclosure method for inverse obstacle scattering problems with dynamical data over a finite time interval:III. Sound-soft obstacle and bistatic data2013

    • Author(s)
      Ikehata, M.
    • Journal Title

      Inverse Problems

      Volume: 29 Issue: 8 Pages: 085013-085013

    • DOI

      10.1088/0266-5611/29/8/085013

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Presentation] The enclosure method for inverse obstacle scattering over a finite time interval: IV. Extraction from a single point on the graph of the response operator2017

    • Author(s)
      Masaru Ikehata
    • Organizer
      Inverse problems for partial differential equations
    • Place of Presentation
      京都大学数理解析研究所, 京都
    • Year and Date
      2017-01-26
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] The probe and enclosure methods for inverse obstacle problems governed by partial differential equations2016

    • Author(s)
      Masaru Ikehata
    • Organizer
      ICUB Talks:Exact Sciences Section
    • Place of Presentation
      ICUB, Univ. Bucharest, Bucharest, Romania
    • Year and Date
      2016-11-10
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] The enclosure method for the Maxwell system in time domain2016

    • Author(s)
      Masaru Ikehata
    • Organizer
      Geometry of solutions of PDE's and related inverse problems
    • Place of Presentation
      東北大学, 仙台
    • Year and Date
      2016-10-06
    • Related Report
      2016 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] On finding an obstacle with the Leontovich boundary condition via the time domain enclosure method2016

    • Author(s)
      池畠 優
    • Organizer
      日本数学会2016年度秋季総合分科会函数方程式論分科会
    • Place of Presentation
      関西大学, 大阪
    • Year and Date
      2016-09-17
    • Related Report
      2016 Annual Research Report
  • [Presentation] On finding an obstacle embedded in the rough background medium via the enclosure method in the time domain2016

    • Author(s)
      池畠 優
    • Organizer
      日本数学会2016年度年会函数方程式論分科会
    • Place of Presentation
      筑波大学、茨城
    • Year and Date
      2016-03-19
    • Related Report
      2015 Research-status Report
  • [Presentation] The enclosure method for inverse obstacle scattering in time domain2016

    • Author(s)
      Masaru Ikehata
    • Organizer
      Workshop on Analysis in Kagurazaka 2016
    • Place of Presentation
      Tokyo University of Science, Tokyo, Japan
    • Year and Date
      2016-01-22
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] The enclosure method for inverse obstacle scattering using a solution of the Maxwell system in the time domain2015

    • Author(s)
      池畠 優
    • Organizer
      日本数学会2015年度秋季総合分科会函数方程式論分科会
    • Place of Presentation
      京都産業大学、京都
    • Year and Date
      2015-09-15
    • Related Report
      2015 Research-status Report
  • [Presentation] The enclosure method for the evaluation of the spot welding area using a solution of the Laplace equation2015

    • Author(s)
      池畠 優, 伊藤 弘道、笹本 明
    • Organizer
      日本数学会2015年度秋季総合分科会函数方程式論分科会
    • Place of Presentation
      京都産業大学、京都
    • Year and Date
      2015-09-13
    • Related Report
      2015 Research-status Report
  • [Presentation] The enclosure method for inverse obstacle scattering using a single electromagnetic wave in time domain2015

    • Author(s)
      Masaru Ikehata
    • Organizer
      Minisymposium (M21) Reconstruction methods for inverse problems (Part 1),Applied Inverse Problems Conference AIPC2015
    • Place of Presentation
      University of Helsinki, Helsinki, Finland
    • Year and Date
      2015-05-28
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Some recent results on inverse obstacle scattering in time domain using the enclosure method2015

    • Author(s)
      Ikehata, M.
    • Organizer
      RIMS研究集会「微分方程式の逆問題とその周辺」 (Inverse problems of differential equations and related topics)
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2015-01-28
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] The enclosure method for inverse obstacle scattering using a solution of the Maxwell system in time domain2014

    • Author(s)
      池畠 優
    • Organizer
      熊本大学応用解析セミナー
    • Place of Presentation
      熊本大学
    • Year and Date
      2014-12-13
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] The enclosure method for inverse obstacle scattering using a solution of the Maxwell system in time domain2014

    • Author(s)
      池畠 優
    • Organizer
      大阪大学数学教室微分方程式セミナー
    • Place of Presentation
      大阪大学
    • Year and Date
      2014-10-31
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] 時間領域における波の物体散乱の逆問題と囲い込み法2014

    • Author(s)
      池畠 優
    • Organizer
      日本応用数理学会2014年度年会 セッション「逆問題と信号処理」
    • Place of Presentation
      政策研究大学院大学
    • Year and Date
      2014-09-03
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] The enclosure method for inverse obstacle scattering in time domain2014

    • Author(s)
      Ikehata, M.
    • Organizer
      Minisymposium (M8) Analytical and Numerical Methods for Inverse Problems, 7th International Conference ``Inverse Problems: Modeling and Simulation''
    • Place of Presentation
      Oldeniz-Fethiye, Turkey
    • Year and Date
      2014-05-28
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] On reconstruction of cavities in a three dimensional linearized viscoelasticity2014

    • Author(s)
      Ikehata, M. and Itou, H.
    • Organizer
      Minisymposium (M14) Non-iterative reconstruction schemes for inverse problems, 7th International Conference ``Inverse Problems: Modeling and Simulation''
    • Place of Presentation
      Oldeniz-Fethiye, Turkey
    • Year and Date
      2014-05-28
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] The enclosure method for an inverse obstacle scattering problem with dynamical bistatic data over a finite time interval

    • Author(s)
      池畠優
    • Organizer
      愛媛大学解析セミナー
    • Place of Presentation
      愛媛大学解析セミナー
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] The enclosure method using dynamical data

    • Author(s)
      Ikehata, M.
    • Organizer
      Applied Inverse Problem Conference
    • Place of Presentation
      Korea Advanced Institute for Sciences and Tecnology, Daejeon, Korea
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] The Enclosure Method for Inverse Obstacle Scattering

    • Author(s)
      池畠優
    • Organizer
      研究集会「第9回非線型の諸問題」
    • Place of Presentation
      高知大学(高知県)
    • Related Report
      2013 Research-status Report
    • Invited
  • [Remarks]

    • URL

      https://www.researchgate.net/profile/Masaru_Ikehata

    • Related Report
      2016 Annual Research Report
  • [Remarks] ResearchGate

    • URL

      https://www.researchgate.net/profile/Masaru_Ikehata

    • Related Report
      2015 Research-status Report
  • [Remarks] Masaru Ikehata- ResearchGate

    • URL

      http://www.researchgate.net/profile/Masaru_Ikehata

    • Related Report
      2014 Research-status Report
  • [Remarks] Masaru Ikehata - ResearchGate

    • URL

      http://www.researchgate.net/profile/Masaru_Ikehata

    • Related Report
      2013 Research-status Report

URL: 

Published: 2014-07-25   Modified: 2019-07-29  

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