• Search Research Projects
  • Search Researchers
  • How to Use
  1. Back to previous page

Mathematical Analysis on dynamic rupture problems and its seismological application

Research Project

Project/Area Number 18K03380
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Review Section Basic Section 12020:Mathematical analysis-related
Research InstitutionTokyo University of Science

Principal Investigator

Itou Hiromichi  東京理科大学, 理学部第二部数学科, 教授 (30400790)

Co-Investigator(Kenkyū-buntansha) 田中 良巳  横浜国立大学, 大学院環境情報研究院, 教授 (10315830)
Project Period (FY) 2018-04-01 – 2023-03-31
Project Status Completed (Fiscal Year 2022)
Budget Amount *help
¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2022: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2021: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2020: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2019: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2018: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Keywords動弾性体 / き裂 / 摩擦 / 接触問題 / 逆問題 / 非線形弾性体 / 粘弾性体 / 多孔性媒質 / 非貫通条件 / 断層破壊 / Boussinesq問題 / 動的破壊問題 / 動的破壊 / 自己相似解
Outline of Final Research Achievements

In this study, we consider a mathematical model that incorporates the unique properties of the earthquake progression process, such as scale invariance and energy dissipation due to friction. As a result, a qualitative theory for an initial value boundary value problem with a given friction force and a generalized non-penetration condition (named SCD condition) on a fixed crack surface in a linear dynamic elastic body is obtained. As an application to seismology, an indication formula for the slip velocity was derived for a problem in which several friction conditions are imposed on a self-similarly expanding crack. Furthermore, the method for the inverse crack problems in elastic bodies was developed, and a mathematical theory for the crack problem was constructed for a new elastic model describing porous media such as concrete and rock.

Academic Significance and Societal Importance of the Research Achievements

線形動弾性体におけるき裂問題に摩擦条件と接触条件を課した問題については未解決なことが多かったが、現象に見合ったき裂面における摩擦条件や接触条件を考察し、数学理論を発展させた。これらは今後、地震学で用いられている摩擦モデルの理論的解析に貢献できると考えられる。また、地震の特徴を組み込んだ数理モデルの解析解の導出は地震学における破壊伝播速度の決定機構の解明につながるものである。さらに、非破壊検査に関連するき裂の逆問題および多孔質弾性体を記述する新しい数理モデルにおけるき裂問題の数学解析で得られた成果は工学分野への波及効果が期待できる。

Report

(6 results)
  • 2022 Annual Research Report   Final Research Report ( PDF )
  • 2021 Research-status Report
  • 2020 Research-status Report
  • 2019 Research-status Report
  • 2018 Research-status Report
  • Research Products

    (64 results)

All 2022 2021 2020 2019 2018 Other

All Int'l Joint Research (21 results) Journal Article (14 results) (of which Int'l Joint Research: 11 results,  Peer Reviewed: 12 results,  Open Access: 12 results) Presentation (21 results) (of which Int'l Joint Research: 10 results,  Invited: 14 results) Book (1 results) Remarks (1 results) Funded Workshop (6 results)

  • [Int'l Joint Research] University of Graz(オーストリア)

    • Related Report
      2022 Annual Research Report
  • [Int'l Joint Research] Novosibirsk state University/Institute of hydrodynamics/North-Eastern Federal University(ロシア連邦)

    • Related Report
      2022 Annual Research Report
  • [Int'l Joint Research] Texas A&M University(米国)

    • Related Report
      2022 Annual Research Report
  • [Int'l Joint Research] Aix-Marseille University/University of Toulouse(フランス)

    • Related Report
      2022 Annual Research Report
  • [Int'l Joint Research] University of Graz(オーストリア)

    • Related Report
      2021 Research-status Report
  • [Int'l Joint Research] Novosibirsk state University/Institute of hydrodynamics(ロシア連邦)

    • Related Report
      2021 Research-status Report
  • [Int'l Joint Research] Texas A&M University(米国)

    • Related Report
      2021 Research-status Report
  • [Int'l Joint Research] University of Graz(オーストリア)

    • Related Report
      2020 Research-status Report
  • [Int'l Joint Research] Novosibirsk state University/Institute of hydrodynamics(ロシア連邦)

    • Related Report
      2020 Research-status Report
  • [Int'l Joint Research] Texas A&M University(米国)

    • Related Report
      2020 Research-status Report
  • [Int'l Joint Research] University of Graz(オーストリア)

    • Related Report
      2019 Research-status Report
  • [Int'l Joint Research] Texas A&M University(米国)

    • Related Report
      2019 Research-status Report
  • [Int'l Joint Research] Novosibirsk state University/Institute of hydrodynamics(ロシア連邦)

    • Related Report
      2019 Research-status Report
  • [Int'l Joint Research] University of Helsinki(フィンランド)

    • Related Report
      2019 Research-status Report
  • [Int'l Joint Research] Chinese Academy of Sciences(中国)

    • Related Report
      2019 Research-status Report
  • [Int'l Joint Research] University of Graz(オーストリア)

    • Related Report
      2018 Research-status Report
  • [Int'l Joint Research] Texas A&M University(米国)

    • Related Report
      2018 Research-status Report
  • [Int'l Joint Research] Novosibirsk state University/Institute of hydrodynamics(ロシア連邦)

    • Related Report
      2018 Research-status Report
  • [Int'l Joint Research] University of Helsinki(フィンランド)

    • Related Report
      2018 Research-status Report
  • [Int'l Joint Research] University College London(英国)

    • Related Report
      2018 Research-status Report
  • [Int'l Joint Research]

    • Related Report
      2018 Research-status Report
  • [Journal Article] Unique solvability of a crack problem with Signorini-type and Tresca friction conditions in a linearized elastodynamic body2022

    • Author(s)
      Kashiwabara Takahito、Itou Hiromichi
    • Journal Title

      Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences

      Volume: 380 Issue: 2236 Pages: 20220225-20220225

    • DOI

      10.1098/rsta.2022.0225

    • Related Report
      2022 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Investigation of implicit constitutive relations in which both the stress and strain appear linearly, adjacent to non-penetrating cracks2022

    • Author(s)
      Itou Hiromichi、Kovtunenko Victor A.、Rajagopal Kumbakonam R.
    • Journal Title

      Mathematical Models and Methods in Applied Sciences

      Volume: 32 Issue: 07 Pages: 1475-1492

    • DOI

      10.1142/s0218202522500336

    • Related Report
      2022 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Asymptotic series solution for plane poroelastic model with non-penetrating crack driven by hydraulic fracture2022

    • Author(s)
      Itou Hiromichi、Kovtunenko Victor A.、Lazarev Nyurgun P.
    • Journal Title

      Applications in Engineering Science

      Volume: 10 Pages: 100089-100089

    • DOI

      10.1016/j.apples.2022.100089

    • Related Report
      2022 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] On an Implicit Model Linear in Both Stress and Strain to Describe the Response of Porous Solids2021

    • Author(s)
      Itou Hiromichi、Kovtunenko Victor A.、Rajagopal Kumbakonam R.
    • Journal Title

      Journal of Elasticity

      Volume: 144 Issue: 1 Pages: 107-118

    • DOI

      10.1007/s10659-021-09831-x

    • Related Report
      2021 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Three-field mixed formulation of elasticity model nonlinear in the mean normal stress for the problem of non-penetrating cracks in bodies2021

    • Author(s)
      Itou Hiromichi、Kovtunenko Victor A.、Rudoy Evgeny M.
    • Journal Title

      Applications in Engineering Science

      Volume: 7 Pages: 100060-100060

    • DOI

      10.1016/j.apples.2021.100060

    • Related Report
      2021 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Unique solvability of crack problem with time-dependent friction condition in linearized elastodynamic body2021

    • Author(s)
      Itou Hiromichi、Kashiwabara Takahito
    • Journal Title

      Mathematical notes of NEFU

      Volume: 28 Issue: 3(111) Pages: 121-134

    • DOI

      10.25587/svfu.2021.38.33.008

    • Related Report
      2021 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] Lagrange multiplier approach to unilateral indentation problems: Well-posedness and application to linearized viscoelasticity with non-invertible constitutive response2021

    • Author(s)
      Itou Hiromichi、Kovtunenko Victor A.、Rajagopal Kumbakonam R.
    • Journal Title

      Mathematical Models and Methods in Applied Sciences

      Volume: - Issue: 03 Pages: 1-26

    • DOI

      10.1142/s0218202521500159

    • Related Report
      2020 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] On unilateral contact problems with friction for an elastic body with cracks2021

    • Author(s)
      Furtsev Alexey I.、Itou Hiromichi、Kovtunenko Victor A.、Rudoy Evgeny M.、Tani Atusi
    • Journal Title

      RIMS Kokyuroku

      Volume: 2174 Pages: 43-58

    • NAID

      120007142218

    • Related Report
      2020 Research-status Report
    • Int'l Joint Research
  • [Journal Article] Proceedings of 45th Sapporo Symposium on Partial Differential Equations2020

    • Author(s)
      Itou Hiromichi
    • Journal Title

      Hokkaido University technical report series in Mathematics

      Volume: 179 Pages: 1-98

    • DOI

      10.14943/94913

    • NAID

      120006875081

    • Year and Date
      2020-07-30
    • Related Report
      2020 Research-status Report
    • Open Access
  • [Journal Article] The Boussinesq flat-punch indentation problem within the context of linearized viscoelasticity2020

    • Author(s)
      Itou Hiromichi、Kovtunenko Victor A.、Rajagopal Kumbakonam R.
    • Journal Title

      International Journal of Engineering Science

      Volume: 151 Pages: 103272-103272

    • DOI

      10.1016/j.ijengsci.2020.103272

    • Related Report
      2019 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] A priori estimates for the general dynamic Euler?Bernoulli beam equation: Supported and cantilever beams2019

    • Author(s)
      Hasanov Alemdar、Itou Hiromichi
    • Journal Title

      Applied Mathematics Letters

      Volume: 87 Pages: 141-146

    • DOI

      10.1016/j.aml.2018.07.038

    • Related Report
      2018 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Crack problem within the context of implicitly constituted quasi-linear viscoelasticity2019

    • Author(s)
      Itou Hiromichi、Kovtunenko Victor A.、Rajagopal Kumbakonam R.
    • Journal Title

      Mathematical Models and Methods in Applied Sciences

      Volume: 29 Issue: 02 Pages: 355-372

    • DOI

      10.1142/s0218202519500118

    • Related Report
      2018 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Revealing cracks inside conductive bodies by electric surface measurements2019

    • Author(s)
      Hauptmann, A., Ikehata, M, Itou, H. and Siltanen, S.
    • Journal Title

      Inverse Problems

      Volume: 35 Issue: 2 Pages: 025004-025004

    • DOI

      10.1088/1361-6420/aaf273

    • Related Report
      2018 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Well-posedness of the problem of non-penetrating cracks in elastic bodies whose material moduli depend on the mean normal stress2019

    • Author(s)
      Itou Hiromichi、Kovtunenko Victor A.、Rajagopal Kumbakonam R.
    • Journal Title

      International Journal of Engineering Science

      Volume: 136 Pages: 17-25

    • DOI

      10.1016/j.ijengsci.2018.12.005

    • Related Report
      2018 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Presentation] On inverse crack problems in linearized elastic bodies by the Enclosure method2022

    • Author(s)
      Hiromichi Itou
    • Organizer
      Theoretical and numerical trends in inverse problems and control for PDE's, and Hamilton-Jacobi equation: French-Italian-Japanese conference
    • Related Report
      2022 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] 囲い込み法を用いた線形弾性体におけるき裂の再構成について2022

    • Author(s)
      池畠優、伊藤弘道
    • Organizer
      日本応用数理学会2022年度年会
    • Related Report
      2022 Annual Research Report
    • Invited
  • [Presentation] A remark on crack problems with time-dependent friction condition in linearized elastodynamic body2022

    • Author(s)
      Itou Hiromichi、Kashiwabara Takahito
    • Organizer
      The XXIII International Symposium on Mathematical Methods Applied to Science (XXIII SIMMAC)
    • Related Report
      2021 Research-status Report
    • Int'l Joint Research
  • [Presentation] 速度を含むSignorini型接触条件とTresca摩擦条件下での線形動弾性体方程式の一意可解性2022

    • Author(s)
      柏原崇人、伊藤弘道
    • Organizer
      日本数学会2022年度年会 函数方程式論分科会
    • Related Report
      2021 Research-status Report
  • [Presentation] き裂問題の数学解析-摩擦・接触、非線形弾性体-2021

    • Author(s)
      伊藤弘道
    • Organizer
      Elastic and dissipative motions of curves and interfaces in continuum media
    • Related Report
      2021 Research-status Report
  • [Presentation] On an inverse crack problem in a linearized elasticity by the enclosure method2021

    • Author(s)
      Itou Hiromichi
    • Organizer
      The 8th European congress of Mathematics, Nonsmooth Variational Methods for PDEs and Applications in Mechanics (MS - ID 8)
    • Related Report
      2021 Research-status Report
    • Int'l Joint Research
  • [Presentation] ある非線形(粘)弾性体モデルの数学解析2021

    • Author(s)
      伊藤弘道
    • Organizer
      幾何学・連続体力学・情報科学の交差領域の探索(II)
    • Related Report
      2021 Research-status Report
    • Invited
  • [Presentation] On unilateral indentation problems in viscoelasticity with non-invertible constitutive response2021

    • Author(s)
      Itou Hiromichi
    • Organizer
      Critical Exponent and Nonlinear Partial Differential Equations 2021
    • Related Report
      2020 Research-status Report
    • Invited
  • [Presentation] On a flat-punch indentation problem within the context of linearized viscoelasticity2020

    • Author(s)
      Itou Hiromichi
    • Organizer
      The Second Russia-Japan Workshop "Mathematical analysis of fracture phenomena for elastic structures and its applications" - 20th Conference of Continuum Mechanics Focusing on Singularities (CoMFoS20)
    • Related Report
      2020 Research-status Report
    • Int'l Joint Research
  • [Presentation] 粘弾性体におけるき裂問題と圧子押込み問題について2020

    • Author(s)
      伊藤弘道
    • Organizer
      第32回さいたま数理解析セミナー
    • Related Report
      2020 Research-status Report
    • Invited
  • [Presentation] 弾性体における摩擦を伴う接触問題について2020

    • Author(s)
      伊藤弘道
    • Organizer
      第724回応用解析研究会
    • Related Report
      2020 Research-status Report
    • Invited
  • [Presentation] On flat-punch indentation problems within the context of linearized viscoelasticity2020

    • Author(s)
      Itou Hiromichi、Kovtunenko Victor A.、Rajagopal Kumbakonam R.
    • Organizer
      日本数学会2020年度秋季総合分科会 函数方程式論分科会
    • Related Report
      2020 Research-status Report
  • [Presentation] On an inverse crack problem in a linearized elasticity by the enclosure method2020

    • Author(s)
      伊藤弘道
    • Organizer
      第45回偏微分方程式論札幌シンポジウム
    • Related Report
      2020 Research-status Report
    • Invited
  • [Presentation] On some problems within the context of implicitly constituted (visco)elasticity with limiting small strain2020

    • Author(s)
      伊藤弘道
    • Organizer
      松山解析セミナー2020
    • Related Report
      2019 Research-status Report
    • Invited
  • [Presentation] On unilateral contact problems with friction for an elastic body with cracks2020

    • Author(s)
      Hiromichi Itou
    • Organizer
      RIMS共同研究(公開型)「偏微分方程式による逆問題解析とその周辺」
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] On some problems for fracture phenomena2019

    • Author(s)
      Hiromichi Itou
    • Organizer
      Russia-Japan Workshop “Mathematical analysis of fracture phenomena for elastic structures and its applications”
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research
  • [Presentation] Detecting cracks in conductive bodies by the enclosure method2019

    • Author(s)
      Hiromichi Itou
    • Organizer
      International Conference AIP2019: Applied Inverse Problems conference
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] On Crack Problems for Nonlinear (Visco)Elasticity2019

    • Author(s)
      Hiromichi Itou
    • Organizer
      International Conference AIP2019: Applied Inverse Problems conference
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] On inverse crack problems in conductive bodies by the enclosure method2019

    • Author(s)
      Hiromichi Itou
    • Organizer
      The 11th Conference on Inverse Problems, Imaging and Applications
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] On an interfacial self-similar crack problem in anti-plane deformation2018

    • Author(s)
      Hiromichi Itou
    • Organizer
      9th International Conference IP:M&S (Inverse Problems: Modeling and Simulation)
    • Related Report
      2018 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] ある非線形(粘) 弾性体におけるき裂問題について2018

    • Author(s)
      伊藤弘道
    • Organizer
      大分微分方程式研究集会
    • Related Report
      2018 Research-status Report
    • Invited
  • [Book] Mathematical Analysis of Continuum Mechanics and Industrial Applications III -Proceedings of the International Conference CoMFoS18- (Mathematics for Industry Volume 34)2020

    • Author(s)
      Itou, H., Hirano, S., Kimura, M., Kovtunenko, V.A., Khludnev, A.M. (Eds.)
    • Total Pages
      204
    • Publisher
      Springer
    • Related Report
      2020 Research-status Report
  • [Remarks] HIROMICHI ITOU

    • URL

      http://www.rs.tus.ac.jp/h-itou/

    • Related Report
      2022 Annual Research Report 2021 Research-status Report 2020 Research-status Report 2019 Research-status Report 2018 Research-status Report
  • [Funded Workshop] 若手研究集会「波動・振動・流れの制御と逆問題 -理論と数値計算-」2022

    • Related Report
      2022 Annual Research Report
  • [Funded Workshop] Workshop for young scholars Control and inverse problems on waves, oscillations and flows - Mathematical analysis and computational methods -2021

    • Related Report
      2021 Research-status Report
  • [Funded Workshop] 「数理モデリングと数学解析研究部門」セミナー『逆問題と機械学習』2020

    • Related Report
      2019 Research-status Report
  • [Funded Workshop] 若手研究集会「波動・振動・流れの制御と逆問題 -理論と数値計算-」2019

    • Related Report
      2019 Research-status Report
  • [Funded Workshop] International Conference CoMFoS18: Mathematical Analysis of Continuum Mechanics II2018

    • Related Report
      2018 Research-status Report
  • [Funded Workshop] Inverse Problems for Partial Differential Equations2018

    • Related Report
      2018 Research-status Report

URL: 

Published: 2018-04-23   Modified: 2024-01-30  

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi