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The effect of scale factor on nonlinear waves in the expanding universe model

Research Project

Project/Area Number 18K03351
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 InstitutionHirosaki University

Principal Investigator

Tsutaya Kimitoshi  弘前大学, 理工学研究科, 教授 (60250411)

Project Period (FY) 2018-04-01 – 2024-03-31
Project Status Completed (Fiscal Year 2023)
Budget Amount *help
¥2,600,000 (Direct Cost: ¥2,000,000、Indirect Cost: ¥600,000)
Fiscal Year 2020: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
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波動方程式 / 時間大域解存在 / 爆発解 / 解の存在時間 / スケール因子 / 膨張宇宙 / 消散効果 / 初期値問題 / 一様等方宇宙モデル
Outline of Final Research Achievements

We study nonlinear waves in the Friedmann-Lemaitre-Robertson-Walker spacetime, known as the standard cosmological model. The aim of this study is to elucidate the effect of the scale factor, representing the expansion rate of the universe, on nonlinear waves by comparing with known results in flat spacetime, such as the Minkowski spacetime. We classify the expanding universe model into decelerating, constant,and accelerating cases, and determine the global existence conditions, blow-up conditions, and estimates for the lifespan of blow-up solutions of the nonlinear wave equation. As a result, it is revealed that blow-up of solutions is more likely to occur compared to the Minkowski spacetime case, and furthermore, the lifespan of blow-up solutions is shorter.

Academic Significance and Societal Importance of the Research Achievements

標準宇宙モデルとして重要なフリードマン・ルメートル・ロバートソン・ウォーカー時空を背景時空とした非線形波動方程式を解析した結果,このような膨張宇宙モデルでは,平坦なミンコフスキー時空と比べ,非線形波動の特異性の発生が起こりやすいことを数学的解析により明らかにした.つまり,膨張宇宙モデルにおいては膨張速度が波動の挙動に大きな影響を及ぼしているということがわかった.今後の非線形波動方程式研究を進めるための指針を提供した.

Report

(7 results)
  • 2023 Annual Research Report   Final Research Report ( PDF )
  • 2022 Research-status Report
  • 2021 Research-status Report
  • 2020 Research-status Report
  • 2019 Research-status Report
  • 2018 Research-status Report
  • Research Products

    (17 results)

All 2024 2023 2022 2021 2020 2019

All Journal Article (7 results) (of which Peer Reviewed: 7 results,  Open Access: 1 results) Presentation (10 results) (of which Int'l Joint Research: 1 results,  Invited: 3 results)

  • [Journal Article] Remarks on Blow up of Solutions of Nonlinear Wave Equations in Friedmann-Lemaitre-Robertson-Walker Spacetime2024

    • Author(s)
      Kimitoshi Tsutaya and Yuta Wakasugi
    • Journal Title

      Mathematical Physics and Its Interactions, Springer Proceedings in Mathematics & Statistics

      Volume: 451 Pages: 181-197

    • DOI

      10.1007/978-981-97-0364-7_6

    • ISBN
      9789819703630, 9789819703647
    • Related Report
      2023 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Blow up of solutions of semilinear wave equations with time-dependent propagation speed and damping2024

    • Author(s)
      Kimitoshi Tsutaya and Yuta Wakasugi
    • Journal Title

      Proceedings of Mathematical Analysis of Nonlinear Dispersive and Wave Equations

      Volume: -

    • Related Report
      2023 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On Glassey’s conjecture for semilinear wave equations in Friedmann-Lemaitre-Robertson-Walker spacetime2021

    • Author(s)
      Tsutaya Kimitoshi、Wakasugi Yuta
    • Journal Title

      Boundary Value Problems

      Volume: 2021 Issue: 1 Pages: 1-30

    • DOI

      10.1186/s13661-021-01571-0

    • Related Report
      2021 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] Blow-up of solutions of semilinear wave equations in accelerated expanding Friedmann-Lemaitre-Robertson-Walker spacetime2021

    • Author(s)
      Tsutaya Kimitoshi、Wakasugi Yuta
    • Journal Title

      Reviews in Mathematical Physics

      Volume: 34 Issue: 02 Pages: 2250003-2250003

    • DOI

      10.1142/s0129055x22500039

    • Related Report
      2021 Research-status Report
    • Peer Reviewed
  • [Journal Article] Blow up of solutions of semilinear wave equations related to nonlinear waves in de Sitter spacetime2021

    • Author(s)
      Tsutaya Kimitoshi、Wakasugi Yuta
    • Journal Title

      Partial Differential Equations and Applications

      Volume: 3 Issue: 1 Pages: 1-10

    • DOI

      10.1007/s42985-021-00145-0

    • Related Report
      2021 Research-status Report
    • Peer Reviewed
  • [Journal Article] On heatlike lifespan of solutions of semilinear wave equations in Friedmann-Lema^itre-Robertson-Walker spacetime2021

    • Author(s)
      Tsutaya Kimitoshi、Wakasugi Yuta
    • Journal Title

      Journal of Mathematical Analysis and Applications

      Volume: 500 Issue: 2 Pages: 125133-125133

    • DOI

      10.1016/j.jmaa.2021.125133

    • Related Report
      2020 Research-status Report
    • Peer Reviewed
  • [Journal Article] Blow up of solutions of semilinear wave equations in Friedmann-Lema^itre-Robertson-Walker spacetime2020

    • Author(s)
      Tsutaya Kimitoshi、Wakasugi Yuta
    • Journal Title

      Journal of Mathematical Physics

      Volume: 61 Issue: 9 Pages: 091503-091503

    • DOI

      10.1063/1.5139301

    • Related Report
      2020 Research-status Report
    • Peer Reviewed
  • [Presentation] Blow up of solutions of semilinear wave equations with time-dependent propagation speed and damping2024

    • Author(s)
      津田谷公利
    • Organizer
      The 25th Northeastern Symposium on Mathematical Analysis
    • Related Report
      2023 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Blow up of solutions of semilinear wave equations with time-dependent damping2023

    • Author(s)
      津田谷公利,若杉勇太
    • Organizer
      日本数学会
    • Related Report
      2022 Research-status Report
  • [Presentation] On Glassey's conjecture for nonlinear wave equations in Friedmann-Lemaitre-Robertson-Walker spacetime2022

    • Author(s)
      津田谷公利
    • Organizer
      東北大学応用数理解析セミナー
    • Related Report
      2022 Research-status Report
    • Invited
  • [Presentation] On Glassey's conjecture for semilinear wave equations in FLRW spacetime2021

    • Author(s)
      津田谷公利,若杉勇太
    • Organizer
      日本数学会
    • Related Report
      2021 Research-status Report
  • [Presentation] Blow up of solutions of space derivative nonlinear wave equations in FLRW spacetime2021

    • Author(s)
      津田谷公利,若杉勇太
    • Organizer
      日本数学会
    • Related Report
      2021 Research-status Report
  • [Presentation] Blow up of solutions of semilinear wave equations in de Sitter spacetime2021

    • Author(s)
      津田谷公利,若杉勇太
    • Organizer
      日本数学会
    • Related Report
      2021 Research-status Report
  • [Presentation] On heatlike lifespan of solutions of semilinear wave equations in Friedmann-Lema^itre-Robertson-Walker spacetime2021

    • Author(s)
      津田谷公利,若杉勇太
    • Organizer
      日本数学会
    • Related Report
      2020 Research-status Report
  • [Presentation] Blow up of solutions of semilinear wave equations related to nonlinear waves in accelerated expanding FLRW spacetime2021

    • Author(s)
      津田谷公利,若杉勇太
    • Organizer
      日本数学会
    • Related Report
      2020 Research-status Report
  • [Presentation] Blow up of solutions of semilinear wave equations with scale-invariant damping relevant to nonlinear waves in FLRW spacetime2019

    • Author(s)
      津田谷公利
    • Organizer
      日本数学会
    • Related Report
      2019 Research-status Report
  • [Presentation] Blow up of solutions of semilinear wave equations with scale-invariant damping relevant to nonlinear waves in FLRW spacetime2019

    • Author(s)
      津田谷公利
    • Organizer
      北海道大学偏微分方程式セミナー
    • Related Report
      2019 Research-status Report
    • Invited

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Published: 2018-04-23   Modified: 2025-01-30  

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