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Global behavior of solutions to nonlinear wave equations with dissipative structures

Research Project

Project/Area Number 16K17625
Research Category

Grant-in-Aid for Young Scientists (B)

Allocation TypeMulti-year Fund
Research Field Mathematical analysis
Research InstitutionHiroshima University (2019-2021)
Ehime University (2016-2018)

Principal Investigator

Wakasugi Yuta  広島大学, 先進理工系科学研究科(工), 准教授 (20771140)

Project Period (FY) 2016-04-01 – 2022-03-31
Project Status Completed (Fiscal Year 2021)
Budget Amount *help
¥3,120,000 (Direct Cost: ¥2,400,000、Indirect Cost: ¥720,000)
Fiscal Year 2019: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2018: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2017: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2016: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Keywords消散型波動方程式 / 時間大域解 / 漸近挙動 / 解の爆発 / 臨界指数 / FLRW計量 / Navier-Stokes方程式 / 消散型梁方程式 / 非線形消散型波動方程式 / 時間大域的適切性 / 解の大域挙動 / エネルギー臨界 / 集約的非線形項
Outline of Final Research Achievements

For linear and nonlinear wave equation with dissipative structures, the existence of the global solution, the asymptotic behavior of the solution, and the finite time blow-up of the solutions are studied. In particular, for damped wave equation with variable coefficients and the nonlinear wave equation in FLRW spacetime, which is a model of homogeneous, isotropic, and expanding universe, we clarify how the dissipative structure of the equation affects the behavior of the solution.

Academic Significance and Societal Importance of the Research Achievements

波動方程式は,水面の波や音波,光などの波が空間内をどのように伝播するのかを記述する偏微分方程式である.実際の波動現象は,抵抗などの効果で次第に減衰するが,波動方程式にこの効果を加えたものが消散型波動方程式である.本研究ではこの消散型波動方程式に対し,様々な形の消散効果を考え,それらが解の振る舞いにどのように影響を与えるのかを明らかにした.また,相対性理論に現れる膨張・収縮する宇宙モデルにおける波の伝播を考えると,消散構造をもつ波動方程式が現れる.本研究ではさらにこのような宇宙モデルにおいて消散構造が波の振る舞いにどのように影響を及ぼすかを明らかにした.

Report

(7 results)
  • 2021 Annual Research Report   Final Research Report ( PDF )
  • 2020 Research-status Report
  • 2019 Research-status Report
  • 2018 Research-status Report
  • 2017 Research-status Report
  • 2016 Research-status Report
  • Research Products

    (62 results)

All 2022 2021 2020 2019 2018 2017 2016 Other

All Int'l Joint Research (3 results) Journal Article (24 results) (of which Peer Reviewed: 24 results,  Open Access: 4 results,  Acknowledgement Compliant: 1 results) Presentation (34 results) (of which Int'l Joint Research: 6 results,  Invited: 18 results) Remarks (1 results)

  • [Int'l Joint Research] Imam Abdulrahman Bin Faisal University(サウジアラビア)

    • Related Report
      2021 Annual Research Report
  • [Int'l Joint Research] Imam Abdulrahman Bin Faisal University(サウジアラビア)

    • Related Report
      2020 Research-status Report
  • [Int'l Joint Research] TU Bergakademie Freiberg(ドイツ)

    • Related Report
      2016 Research-status Report
  • [Journal Article] Energy-conserving finite difference schemes for nonlinear wave equations with dynamic boundary conditions2022

    • Author(s)
      Umeda Akihiro、Wakasugi Yuta、Yoshikawa Shuji
    • Journal Title

      Applied Numerical Mathematics

      Volume: 171 Pages: 1-22

    • DOI

      10.1016/j.apnum.2021.08.009

    • Related Report
      2021 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 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Unconditional well-posedness for the energy-critical nonlinear damped wave equation2021

    • Author(s)
      Inui Takahisa、Wakasugi Yuta
    • Journal Title

      Journal of Evolution Equations

      Volume: 21 Issue: 4 Pages: 5171-5201

    • DOI

      10.1007/s00028-021-00744-9

    • Related Report
      2021 Annual Research 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 Annual Research Report
    • Peer Reviewed
  • [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 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Classification of asymptotic profiles for the Cauchy problem of damped beam equation with two variable coefficients: Effective damping case2021

    • Author(s)
      Yoshikawa Shuji、Wakasugi Yuta
    • Journal Title

      Journal of Differential Equations

      Volume: 272 Pages: 938-957

    • DOI

      10.1016/j.jde.2020.10.008

    • Related Report
      2020 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] Supersolutions for parabolic equations with unbounded or degenerate diffusion coefficients and their applications to some classes of parabolic and hyperbolic equations2021

    • Author(s)
      SOBAJIMA Motohiro、WAKASUGI Yuta
    • Journal Title

      Journal of the Mathematical Society of Japan

      Volume: 73 Issue: 4 Pages: 1091-1128

    • DOI

      10.2969/jmsj/83928392

    • NAID

      130008106924

    • ISSN
      0025-5645, 1881-1167, 1881-2333
    • Related Report
      2020 Research-status Report
    • Peer Reviewed
  • [Journal Article] Lifespan of Solutions for a Weakly Coupled System of Semilinear Heat Equations2020

    • Author(s)
      FUJIWARA Kazumasa、IKEDA Masahiro、WAKASUGI Yuta
    • Journal Title

      Tokyo Journal of Mathematics

      Volume: 43 Issue: 1 Pages: 163-180

    • DOI

      10.3836/tjm/1502179300

    • 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
  • [Journal Article] Movement of time-delayed hot spots in Euclidean space for a degenerate initial state2020

    • Author(s)
      Sakata Shigehiro、Wakasugi Yuta
    • Journal Title

      Discrete & Continuous Dynamical Systems - A

      Volume: 40 Issue: 5 Pages: 2705-2738

    • DOI

      10.3934/dcds.2020147

    • Related Report
      2019 Research-status Report
    • Peer Reviewed
  • [Journal Article] A Remark on the Critical Exponent for the Semilinear Damped Wave Equation on the Half-Space2019

    • Author(s)
      Wakasugi Yuta
    • Journal Title

      Trends in Mathematics

      Volume: - Pages: 389-394

    • DOI

      10.1007/978-3-030-04459-6_37

    • ISBN
      9783030044589, 9783030044596
    • Related Report
      2019 Research-status Report
    • Peer Reviewed
  • [Journal Article] Estimates of Lifespan and Blow-up Rates for the Wave Equation with a Time-dependent Damping and a Power-type Nonlinearity2019

    • Author(s)
      Fujiwara Kazumasa、Ikeda Masahiro、Wakasugi Yuta
    • Journal Title

      Funkcialaj Ekvacioj

      Volume: 62 Issue: 2 Pages: 157-189

    • DOI

      10.1619/fesi.62.157

    • NAID

      130007695611

    • ISSN
      0532-8721
    • Related Report
      2019 Research-status Report
    • Peer Reviewed
  • [Journal Article] Weighted energy estimates for wave equation with space-dependent damping term for slowly decaying initial data2019

    • Author(s)
      Motohiro Sobajima, Yuta Wakasugi
    • Journal Title

      Communications in Contemporary Mathematics

      Volume: 印刷中 Issue: 05 Pages: 1850035-1850035

    • DOI

      10.1142/s0219199718500359

    • Related Report
      2019 Research-status Report
    • Peer Reviewed
  • [Journal Article] Sharp lifespan estimates of blowup solutions to semi-linear wave equations with time-dependent effective damping2019

    • Author(s)
      Ikeda Masahiro、Sobajima Motohiro、Wakasugi Yuta
    • Journal Title

      Journal of Hyperbolic Differential Equations

      Volume: 16 Issue: 03 Pages: 495-517

    • DOI

      10.1142/s0219891619500176

    • Related Report
      2019 Research-status Report
    • Peer Reviewed
  • [Journal Article] Second order asymptotic expansion for wave equations with time- dependent dissipation in one-space dimension2019

    • Author(s)
      Yuta Wakasugi
    • Journal Title

      Advanced Studies in Pure Mathematics

      Volume: 81 Pages: 401-419

    • Related Report
      2019 Research-status Report
    • Peer Reviewed
  • [Journal Article] Global well-posedness for the semilinear wave equation with time dependent damping in the overdamping case2019

    • Author(s)
      Ikeda Masahiro、Wakasugi Yuta
    • Journal Title

      Proceedings of the American Mathematical Society

      Volume: 148 Issue: 1 Pages: 157-172

    • DOI

      10.1090/proc/14297

    • Related Report
      2019 Research-status Report
    • Peer Reviewed
  • [Journal Article] L^p-L^q estimates for the damped wave equation and the critical exponent for the nonlinear problem with slowly decaying data2019

    • Author(s)
      Ikeda Masahiro, Inui Takahisa, Okamoto Mamoru, Wakasugi Yuta
    • Journal Title

      Communications on Pure & Applied Analysis

      Volume: 18 Issue: 4 Pages: 1967-2008

    • DOI

      10.3934/cpaa.2019090

    • Related Report
      2018 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] Critical exponent for the semilinear wave equations with a damping increasing in the far field2018

    • Author(s)
      Nishihara Kenji、Sobajima Motohiro、Wakasugi Yuta
    • Journal Title

      Nonlinear Differential Equations and Applications NoDEA

      Volume: 25 Issue: 6

    • DOI

      10.1007/s00030-018-0546-2

    • Related Report
      2018 Research-status Report
    • Peer Reviewed
  • [Journal Article] Finite energy of generalized suitable weak solutions to the Navier-Stokes equations and Liouville-type theorems in two dimensional domains2018

    • Author(s)
      H. Kozono, Y. Wakasugi, Y. Terasawa
    • Journal Title

      J. Differential Equations

      Volume: 印刷中 Issue: 4 Pages: 1227-1247

    • DOI

      10.1016/j.jde.2018.03.027

    • Related Report
      2018 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] Asymptotic profile of solution for the Cauchy problem of beam equation with variable coefficient2018

    • Author(s)
      Yoshikawa Shuji、Wakasugi Yuta
    • Journal Title

      Applied Mathematics Letters

      Volume: 76 Pages: 236-241

    • DOI

      10.1016/j.aml.2017.09.006

    • Related Report
      2017 Research-status Report
    • Peer Reviewed
  • [Journal Article] Diffusion phenomena for the wave equation with space-dependent damping term growing at infinity2018

    • Author(s)
      Motohiro Sobajima, Yuta Wakasugi
    • Journal Title

      Advances in Differential Equations

      Volume: 23

    • Related Report
      2017 Research-status Report
    • Peer Reviewed
  • [Journal Article] Blow-up of solutions for weakly coupled systems of complex Ginzburg-Landau equations2017

    • Author(s)
      Kazumasa Fujiwara, Masahiro Ikeda, Yuta Wakasugi
    • Journal Title

      Electron. J. Differential Equations

      Volume: 2017, No. 196

    • Related Report
      2017 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] The Cauchy problem for the nonlinear damped wave equation with slowly decaying data2017

    • Author(s)
      Masahiro Ikeda, Takahisa Inui, Yuta Wakasugi
    • Journal Title

      Nonlinear Differential Equations and Applications NoDEA

      Volume: 24 Issue: 2

    • DOI

      10.1007/s00030-017-0434-1

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Presentation] Decay property of solutions to the semilinear wave equation with space-dependent damping and absorbing nonlinearity2022

    • Author(s)
      若杉勇太
    • Organizer
      第11回室蘭非線形解析研究会
    • Related Report
      2021 Annual Research Report
    • Invited
  • [Presentation] Decay property of solutions to the semilinear wave equation with space-dependent damping and absorbing nonlinearity2021

    • Author(s)
      若杉勇太
    • Organizer
      第2回大同大学若手微分方程式セミナー
    • Related Report
      2021 Annual Research Report
    • Invited
  • [Presentation] Blow up of solutions of semilinear wave equations in de Sitter spacetime2021

    • Author(s)
      若杉勇太
    • Organizer
      日本数学会2021年度秋季総合分科会
    • Related Report
      2021 Annual Research Report
  • [Presentation] 吸収型非線形項と空間変数に依存する摩擦項をもつ波動方程式のエネルギー減衰について2021

    • Author(s)
      若杉勇太
    • Organizer
      日本数学会2021年度秋季総合分科会
    • Related Report
      2021 Annual Research Report
  • [Presentation] Global existence and asymptotic behavior for nonlinear damped wave equations on measure spaces2021

    • Author(s)
      若杉勇太
    • Organizer
      香川における偏微分方程式研究会
    • Related Report
      2021 Annual Research Report
  • [Presentation] Global existence and asymptotic behavior for nonlinear damped wave equations on measure spaces2021

    • Author(s)
      Yuta Wakasugi
    • Organizer
      Recent Advances in Nonlinear Evolution Equations
    • Related Report
      2021 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Decay property of solutions to the semilinear wave equation with space-dependent damping and absorbing nonlinearity2021

    • Author(s)
      若杉勇太
    • Organizer
      熊本大学応用解析セミナー
    • Related Report
      2021 Annual Research Report
    • Invited
  • [Presentation] 空間変数に依存する摩擦項をもつ波動方程式の解のエネルギー減衰2021

    • Author(s)
      若杉勇太
    • Organizer
      大阪市立大学談話会
    • Related Report
      2021 Annual Research Report
    • Invited
  • [Presentation] Weighted energy estimates for solutions to the wave equation with space-dependent damping2021

    • Author(s)
      若杉勇太
    • Organizer
      第36回松山キャンプ
    • Related Report
      2020 Research-status Report
  • [Presentation] On heatlike lifespan of solutions of semilinear wave equations in Friedmann-Lemaitre-Robertson-Walker spacetime2021

    • Author(s)
      若杉勇太
    • Organizer
      日本数学会2021年度年会
    • Related Report
      2020 Research-status Report
  • [Presentation] Asymptotic behavior of solutions to elliptic equations with unbounded coefficients of the second order in unbounded domains2021

    • Author(s)
      若杉勇太
    • Organizer
      日本数学会2021年度年会
    • Related Report
      2020 Research-status Report
  • [Presentation] Asymptotic properties of steady solutions to the 3D axisymmetric Navier-Stokes equations with no swirl2021

    • Author(s)
      若杉勇太
    • Organizer
      日本数学会2021年度年会
    • Related Report
      2020 Research-status Report
  • [Presentation] Blow-up of solutions of semilinear wave equations in Friedmann-Lemaitre-Robertson-Walker spacetime2020

    • Author(s)
      Yuta Wakasugi
    • Organizer
      Webinar on Evolution Models, Critical exponent versus blow-up in evolution models
    • Related Report
      2020 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Endpoint Strichartz estimates for the damped wave equation2020

    • Author(s)
      若杉勇太
    • Organizer
      第35回松山キャンプ
    • Related Report
      2019 Research-status Report
  • [Presentation] Lp-Lq estimates for the damped wave equation and the critical exponent for the nonlinear problem with slowly decaying data2019

    • Author(s)
      Yuta Wakasugi
    • Organizer
      12th International ISAAC Congress
    • Related Report
      2019 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Endpoint Strichartz estimate for the damped wave equation and its application2019

    • Author(s)
      若杉勇太
    • Organizer
      Workshop on nonlinear PDE in Numazu
    • Related Report
      2019 Research-status Report
    • Invited
  • [Presentation] 空間変数に依存する摩擦項をもつ波動方程式の解の漸近挙動について2019

    • Author(s)
      若杉勇太
    • Organizer
      愛媛大学解析セミナー
    • Related Report
      2019 Research-status Report
    • Invited
  • [Presentation] 消散型波動方程式に対するLp-Lq評価と非線形問題への応用2019

    • Author(s)
      若杉勇太
    • Organizer
      日本数学会2019年度秋季総合分科会(特別講演)
    • Related Report
      2019 Research-status Report
    • Invited
  • [Presentation] Endpoint Strichartz estimates for the damped wave equation2019

    • Author(s)
      若杉勇太
    • Organizer
      三重偏微分方程式研究集会~西原健二先生の古希を記念して~
    • Related Report
      2019 Research-status Report
    • Invited
  • [Presentation] Asymptotic behavior of solutions to the wave equation with space-dependent damping and slowly decaying data2019

    • Author(s)
      若杉勇太
    • Organizer
      京都大学NLPDEセミナー
    • Related Report
      2019 Research-status Report
    • Invited
  • [Presentation] 空間変数に依存する摩擦項をもつ波動方程式の解の漸近挙動について2019

    • Author(s)
      若杉勇太
    • Organizer
      広島数理解析セミナー
    • Related Report
      2019 Research-status Report
    • Invited
  • [Presentation] Critical exponent for the semilinear wave equations with a damping increasing in the far field2019

    • Author(s)
      若杉勇太
    • Organizer
      日本数学会2019年度年会
    • Related Report
      2018 Research-status Report
  • [Presentation] Asymptotic properties of steady solutions to the 2D Navier-Stokes equations with finite generalized Dirichlet integral2019

    • Author(s)
      若杉勇太
    • Organizer
      日本数学会2019年度年会
    • Related Report
      2018 Research-status Report
  • [Presentation] 時間変数係数をもつ消散型波動方程式の解の2次漸近形について2019

    • Author(s)
      若杉勇太
    • Organizer
      第34回松山キャンプ
    • Related Report
      2018 Research-status Report
  • [Presentation] Asymptotic profiles of solutions for the Cauchy problem of damped beam equation with two variable coefficients2019

    • Author(s)
      若杉勇太
    • Organizer
      RIMS共同研究「反応拡散方程式と非線形分散型方程式の解の挙動」
    • Related Report
      2018 Research-status Report
    • Invited
  • [Presentation] Weighted energy estimates for wave equation with space-dependent damping term for slowly decaying initial data2018

    • Author(s)
      若杉勇太
    • Organizer
      12th AIMS Conference on Dynamical Systems, Differential Equations and Applications
    • Related Report
      2018 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] L^p-L^q estimates for the damped wave equation and the critical exponent for the nonlinear problem with slowly decaying data2018

    • Author(s)
      若杉勇太
    • Organizer
      名古屋微分方程式セミナー
    • Related Report
      2018 Research-status Report
    • Invited
  • [Presentation] Critical exponent for the semilinear wave equation with a damping term depending on time and space variables2018

    • Author(s)
      若杉勇太
    • Organizer
      名古屋偏微分方程式研究集会
    • Related Report
      2018 Research-status Report
  • [Presentation] 線形消散型波動方程式の解の時間減衰評価, 可積分でない初期値を持つ非線形問題の臨界指数2018

    • Author(s)
      池田正弘,若杉勇太,戍亥隆恭,岡本葵
    • Organizer
      日本数学会2018年度年会
    • Related Report
      2017 Research-status Report
  • [Presentation] Asymptotic behavior of solutions to the wave equation with space-dependent damping2017

    • Author(s)
      Yuta Wakasugi
    • Organizer
      The 42nd Sapporo Symposium on Partial Differential Equations
    • Related Report
      2017 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Asymptotic behavior of solutions to the wave equation with space-dependent damping2017

    • Author(s)
      Yuta Wakasugi
    • Organizer
      11th ISAAC Congress (ISAAC2017)
    • Related Report
      2017 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Diffusion phenomena for the wave equation with space-dependent damping term growing at infinity2017

    • Author(s)
      側島基宏,若杉勇太
    • Organizer
      日本数学会2017年度秋季総合分科会
    • Related Report
      2017 Research-status Report
  • [Presentation] Weighted energy estimates for wave equation with space-dependent damping term for slowly decaying initial data2017

    • Author(s)
      側島基宏,若杉勇太
    • Organizer
      日本数学会2017年度秋季総合分科会
    • Related Report
      2017 Research-status Report
  • [Presentation] The Cauchy problem for the nonlinear damped wave equation with slowly decaying data2016

    • Author(s)
      若杉勇太
    • Organizer
      2016年度日本数学会秋季総合分科会
    • Place of Presentation
      関西大学(大阪府・吹田市)
    • Related Report
      2016 Research-status Report
  • [Remarks] wakasugiyuta

    • URL

      https://sites.google.com/site/wakasugiyuta/home

    • Related Report
      2021 Annual Research Report 2020 Research-status Report 2019 Research-status Report 2018 Research-status Report 2017 Research-status Report 2016 Research-status Report

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Published: 2016-04-21   Modified: 2023-01-30  

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