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非線形消散波動方程式の解がもつ波動的性質の解明

Research Project

Project/Area Number 18H01132
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section一般
Review Section Basic Section 12020:Mathematical analysis-related
Research InstitutionTohoku University

Principal Investigator

高村 博之  東北大学, 理学研究科, 教授 (40241781)

Co-Investigator(Kenkyū-buntansha) 池田 正弘  国立研究開発法人理化学研究所, 革新知能統合研究センター, 研究員 (00749690)
若杉 勇太  広島大学, 先進理工系科学研究科(工), 准教授 (20771140)
若狭 恭平  釧路工業高等専門学校, 創造工学科, 講師 (60783404)
Project Period (FY) 2018-04-01 – 2022-03-31
Project Status Granted (Fiscal Year 2021)
Budget Amount *help
¥17,160,000 (Direct Cost: ¥13,200,000、Indirect Cost: ¥3,960,000)
Fiscal Year 2021: ¥2,990,000 (Direct Cost: ¥2,300,000、Indirect Cost: ¥690,000)
Fiscal Year 2020: ¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2019: ¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2018: ¥5,330,000 (Direct Cost: ¥4,100,000、Indirect Cost: ¥1,230,000)
Keywords非線形消散波動方程式 / 初期値問題 / エネルギー解 / ライフスパン / 非線形波動方程式 / 消散波動方程式 / 半線形波動方程式 / 古典解 / lifespan / 半線形消散波動方程式 / べき型半線形項 / スケール不変消散項 / Strauss指数 / 藤田指数 / ライフスパン評価 / 時間大域存在 / 有限時間爆発 / 半線形 / 消散項 / 臨界指数
Outline of Annual Research Achievements

昨年度に引き続き小さな初期値をもつ半線形消散波動方程式に対する初期値問題を、消散項が時間減衰をもつ場合に詳細に解析した。昨年度は、消散項の係数が時間変数の1次より速く減衰する場合には、エルギークラスの解は消散項がない波動方程式のそれと同様に振る舞う、つまり消散効果が全くないことをほぼ完全に明らかにした。今年度は、ちょうど臨界減衰である1次のscale-invariantと言われる状態のときに何が起こっているかを,解の最大存在時間評価,つまり,lifespan 評価
から明らかにすることを行った。なお、1次より遅い減衰の場合には,消散項が時間2階偏導関数の部分を凌駕し、解は対応する半線形熱方程式のそれのように振る舞うことが良く知られていることに注意する.
基本的に大きく分けて三つの研究を行った。一つ目は主たる研究成果で、低次元低べきの非線形項をもつ波動および消散波動方程式に対する初期値問題の解析である。小さい初期値に対してどのくらい長く解が存在するか、という解のlifespan 評価を初期値の条件を分類して精密に導出した。二つ目は、質量項付き消散波動方程式に対する初期値問題の解析である。消散項の時間減衰を波動方程式に近い状態になるように固定した上、質量項の時間減衰を様々な状況に設定して解析し、lifespan の上からの評価を初期値の条件で分類して精密に導出した。三つ目は、消散波動方程式系に対する初期値問題の解析である。これは,昨年度に得られた消散項の時間減衰が強い単独方程式の結果を2×2の系に拡張して、分類条件をlifespan の上からの評価から提示したものである。

Current Status of Research Progress
Current Status of Research Progress

1: Research has progressed more than it was originally planned.

Reason

ここでは前述の研究実績の概要で述べた主たる研究成果に的を絞って述べる。scale-invariatな消散項の係数が特別な値であるとき,それがLiouville 変換によって臨界である2次の時間減衰をもつ質量項に変換されることを用いて,空間1次元では藤田指数が支配する熱的な状態であっても初期速度の全空間での積分量がゼロか非ゼロによって解の最大存在時間の長短が分類されることを示した。これは、臨界減衰をもつ消散項付き半線形波動方程式のエネルギー解に対して、これまでに消散項の係数が大きければ熱方程式のそれに近く藤田臨界指数が支配的で、逆に小さければ波動方程式のそれに近くStrauss型臨界指数が支配的になっているという予想と一部の結果があったが、解のlifespan評価から見るとそうではない、つまり、いかなる場合も消散項なしの解に近い性質をもつことを示唆する非常に興味深い結果となっている。
これは長年、非線形消散波動方程式を分類している研究者達が、時間大域存在か非存在かを分ける臨界冪の指数が半線形熱方程式のそれである藤田指数かそうでないか、というだけで熱方程式に近いか波動方程式に近いかを分類していたことが不十分だったことを証明したことになる。この結果の影響は大きく、類似の方程式を扱っている周辺分野の研究に大きく方向転換を迫るものである。現に、この研究成果が出版される前後、多数の引用論文がプレプリントサバーであるarXivに登場し、現在もその傾向は止まらない。
以上の状況を鑑みて、当該分野にインパクトの大きい結果を導出することができたと判断し、この区分を選択した。

Strategy for Future Research Activity

引き続き今年度得られた結果を、もっと一般の係数を持つ方程式や多次元でこのような状況が唯一発生すると思われる空間2次元に対して拡張することを試みる。また、結果の重要性から、半線形消散波動方程式以外の類似の方程式に対する解析も急ぎ行う。これらは研究分担者はもちろんのこと、マンパワーの不足を補うため、海外を含めた研究協力者達に依頼して共同研究の形で行う予定である。特に、宇宙論に現れる特異係数を持つ双曲型方程式への応用は、物理にも影響を与えるので解析が急がれる。

Report

(2 results)
  • 2019 Annual Research Report
  • 2018 Annual Research Report

Research Products

(68 results)

All 2020 2019 2018 Other

All Int'l Joint Research (4 results) Journal Article (22 results) (of which Int'l Joint Research: 8 results,  Peer Reviewed: 22 results,  Open Access: 2 results) Presentation (41 results) (of which Int'l Joint Research: 14 results,  Invited: 34 results) Funded Workshop (1 results)

  • [Int'l Joint Research] Lishui University(中国)

    • Related Report
      2019 Annual Research Report
  • [Int'l Joint Research] Bari University/Pisa University/Roma University(イタリア)

    • Related Report
      2019 Annual Research Report
  • [Int'l Joint Research] 麗水学院/復旦大学(中国)

    • Related Report
      2018 Annual Research Report
  • [Int'l Joint Research] バーリ大学(イタリア)

    • Related Report
      2018 Annual Research Report
  • [Journal Article] Nonexistence of global solutions for a weakly coupled system of semilinear damped wave equations of derivative type in the scattering case2020

    • Author(s)
      Alessandro Palmieri, Hiroyuki Takamura
    • Journal Title

      Mediterranean J. of Mathematics

      Volume: 17(13)

    • DOI

      10.1007/s00009-019-1445-4

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Global well-posedness for the semilinear wave equation with time dependent damping in the overdamping case2020

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

      Proc. Amer. Math. Soc.

      Volume: 148 Pages: 157-172

    • DOI

      10.1090/proc/14297

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed
  • [Journal Article] The sharp lower bound of the lifespan of solutions to semilinear wave equations with low powers in two space dimensions2019

    • Author(s)
      Takuto Imai, Masakazu Kato, Hiroyuki Takamura, Kyouhei Wakasa
    • Journal Title

      K.Kato & T.Ogawa & T.Ozawa ed. "Asymptotic Analysis for Nonlinear Dispersive and Wave Equations", Advanced Studies in Pure Mathematics

      Volume: 81 Pages: 31-53

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed
  • [Journal Article] The lifespan of solutions of semilinear wave equations with the scale-invariant damping in one space dimension2019

    • Author(s)
      Masakazu Kato, Hiroyuki Takamura, Kyouhei Wakasa
    • Journal Title

      Differential Integral Equations

      Volume: 32(11-12) Pages: 659-678

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Blow-up for a weakly coupled system of semilinear damped wave equations in the scattering case with power nonlinearities2019

    • Author(s)
      Alessandro Palmieri, Hiroyuki Takamura
    • Journal Title

      Nonlinear Analysis, TMA

      Volume: 187 Pages: 467-492

    • DOI

      10.1016/j.na.2019.06.016

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Wave-like blow-up for semilinear wave equations with scattering damping and negative mass term2019

    • Author(s)
      Ning-an Lai, Nico Michele Schiavone, Hiroyuki Takamura
    • Journal Title

      Trends in Mathematics, M.D'Abbicco, M.Ebert, V.Georgiev, T.Ozawa ed., "New Tools for Nonlinear PDEs and Application", Birkhauser, Cham

      Volume: - Pages: 217-240

    • DOI

      10.1007/978-3-030-10937-0_8

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [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

      J. Hyperbolic Differ. Equ.

      Volume: 16 Pages: 495-517

    • DOI

      10.1142/s0219891619500176

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Blow-up phenomena of semilinear wave equations and their weakly coupled systems2019

    • Author(s)
      Masahiro Ikeda, Motohiro Sobajima, Kyohei Wakasa
    • Journal Title

      J. Differential Equations

      Volume: 267 Pages: 5165-5201

    • DOI

      10.1016/j.jde.2019.05.029

    • Related Report
      2019 Annual Research 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)
      Kazumasa Fujiwara, Masahiro Ikeda, Yuta Wakasugi
    • Journal Title

      Funkcial. Ekvac.

      Volume: 62(2) Pages: 157-189

    • NAID

      130007695611

    • Related Report
      2019 Annual Research 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

      Commun. Contemp. Math.

      Volume: 印刷中 Pages: 1850035-1850035

    • DOI

      10.1142/s0219199718500359

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Critical exponent for nonlinear damped wave equations with non-negative potential in 3D2019

    • Author(s)
      Vladimir Georgiev, Hideo Kubo, Kyouhei Wakasa
    • Journal Title

      J. Differential Equations

      Volume: 267(5) Pages: 3271-3288

    • DOI

      10.1016/j.jde.2019.04.004

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Blow-up of solutions to critical semilinear wave equations with variable coefficients2019

    • Author(s)
      Kyouhei Wakasa, Borislav Yordanov
    • Journal Title

      J. Differential Equations

      Volume: 266(9) Pages: 5360-5376

    • DOI

      10.1016/j.jde.2018.10.028

    • Related Report
      2019 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Nonexistence of global solutions of wave equations with weak time-dependent damping and combined nonlinearity2019

    • Author(s)
      N.-A.Lai and H.Takamura
    • Journal Title

      Nonlinear Analysis, RW

      Volume: 45 Pages: 83-96

    • DOI

      10.1016/j.nonrwa.2018.06.008

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Nonexistence of global solutions of nonlinear wave equations with weak time-dependent damping related to Glassey's conjecture2019

    • Author(s)
      N.-A.Lai and H.Takamura
    • Journal Title

      Differential and Integral Equations

      Volume: 32(1-2) Pages: 37-48

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Sharp upper bound for lifespan of solutions to some critical semilinear parabolic, dispersive and hyperbolic equations via a test function method2019

    • Author(s)
      M.Ikeda and M.Sobajima
    • Journal Title

      Nonlinear Analysis

      Volume: 182 Pages: 57-74

    • DOI

      10.1016/j.na.2018.12.009

    • Related Report
      2018 Annual Research 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 and Applied Analysis

      Volume: 18 Pages: 1967-2008

    • DOI

      10.3934/cpaa.2019090

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Remark on upper bound for lifespan of solutions to semilinear evolution equations in a two-dimensional exterior domain2019

    • Author(s)
      M.Ikeda and M.Sobajima
    • Journal Title

      J. Math. Anal. Appl.

      Volume: 470 Pages: 318-326

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed
  • [Journal Article] The sharp estimate of the lifespan for semilinear wave equation with time-dependent damping2019

    • Author(s)
      M.Ikeda and T.Inui
    • Journal Title

      Differential and Integral Equations

      Volume: 32 Pages: 1-36

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed
  • [Journal Article] On the nonexistence of global solutions for critical semilinear wave equations with damping in the scattering case2019

    • Author(s)
      K.Wakasa and B.Yordanov
    • Journal Title

      Nonlinear Analysis, TMA

      Volume: 180 Pages: 67-74

    • DOI

      10.1016/j.na.2018.09.012

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Diffusion phenomena for the wave equation with space-dependent damping term growing at infinity2018

    • Author(s)
      M.Sobajima and Y.Wakasugi
    • Journal Title

      Advances in Differential Equations

      Volume: 23 Pages: 581-614

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

    • Author(s)
      K.NIshihara, M.Sobajima and Y.Wakasugi
    • Journal Title

      NoDEA Nonlinear Differential Equations Appl.

      Volume: 25 Pages: 25-55

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed
  • [Journal Article] 単独非線形波動方程式の一般論とその最適性を支えるモデル方程式2018

    • Author(s)
      高村博之
    • Journal Title

      日本数学会編『数学』

      Volume: 70 Pages: 375-378

    • NAID

      130007930720

    • Related Report
      2018 Annual Research Report
    • Peer Reviewed
  • [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 Annual Research Report
    • Invited
  • [Presentation] 時間依存係数をもつ半線形消散波動方程式の分類2019

    • Author(s)
      高村 博之
    • Organizer
      第17回浜松偏微分方程式研究集会
    • Related Report
      2019 Annual Research Report
    • Invited
  • [Presentation] The lifespan of solutions of semilinear wave equations with the scale-invariant damping in two space dimensions2019

    • Author(s)
      Hiroyuki Takamura
    • Organizer
      2019 Workshop on Geometry and Nonlinear Partial Differential Equations
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Test function method for blow-up phenomena of semilinear wave equations and their weakly coupled system2019

    • Author(s)
      Masahiro Ikeda
    • Organizer
      2019 Workshop on Geometry and Nonlinear Partial Differential Equations
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Blow-up phenomena of semilinear wave equations and their weakly coupled system2019

    • Author(s)
      Masahiro Ikeda
    • Organizer
      Fall Southeastern Sectional Meeting
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Blow-up phenomena of semilinear wave equations and their weakly coupled system2019

    • Author(s)
      Masahiro Ikeda
    • Organizer
      12th ISAAC Congress
    • Related Report
      2019 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Global well-posedness for the wave equation with a time-dependent scale invariant damping and a cubic convolution2019

    • Author(s)
      池田 正弘, 田中 智之, 若狭 恭平
    • Organizer
      日本数学会・2020年度年会
    • Related Report
      2019 Annual Research Report
  • [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 Annual Research 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 Annual Research 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 Annual Research Report
    • Invited
  • [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 Annual Research 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 Annual Research Report
    • Invited
  • [Presentation] Blow-up of solutions to critical semilinear wave equations with variable coefficients2019

    • Author(s)
      若狭 恭平
    • Organizer
      大同大学第1回若手微分方程式セミナー
    • Related Report
      2019 Annual Research Report
    • Invited
  • [Presentation] Lifespan estimates of solutions of semilinear wave equations with the scale invariant damping in one space dimension2019

    • Author(s)
      H.Takamura
    • Organizer
      第36回 九州における偏微分方程式研究集会, 九州大学
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Lifespan estimates of solutions of semilinear wave equationswith the scale invariant damping in one space dimension2019

    • Author(s)
      H.Takamura
    • Organizer
      東北復旦交流事業, 復旦大学(中国)
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] On blowup solutions of semi linear wave equation and their weakly coupled system2019

    • Author(s)
      池田正弘, 側島基宏, 若狭恭平
    • Organizer
      日本数学会・2019年度年会, 東京工業大学
    • Related Report
      2018 Annual Research Report
  • [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, 東京工業大学
    • Related Report
      2018 Annual Research 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, 山口大学
    • Related Report
      2018 Annual Research Report
    • Invited
  • [Presentation] On the blow-up theorem for critical semilinear wave equations2019

    • Author(s)
      若狭恭平
    • Organizer
      MZセミナー, 宮崎大学
    • Related Report
      2018 Annual Research Report
    • Invited
  • [Presentation] スケール不変な消散項付き1次元半線形波動方程式の解の最大存在時間評価2018

    • Author(s)
      高村博之
    • Organizer
      大阪大学微分方程式セミナー
    • Related Report
      2018 Annual Research Report
    • Invited
  • [Presentation] 非線形消散波動方程式の最近の発展2018

    • Author(s)
      高村博之
    • Organizer
      第1回はこだて数理解析研究集会, 公立はこだて未来大学
    • Related Report
      2018 Annual Research Report
    • Invited
  • [Presentation] Lifespan estimates of solutions of semilinear wave equations with the scale invariant damping in one space dimension2018

    • Author(s)
      H.Takamura
    • Organizer
      Seminario di Matematica, バーリ大学(イタリア)
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] 強い時間減衰を伴う消散項付き非線形波動方程式に対する解の波動的な 爆発とlifespan評価2018

    • Author(s)
      高村博之
    • Organizer
      三重における非線形波動方程式研究集会, 三重大学
    • Related Report
      2018 Annual Research Report
    • Invited
  • [Presentation] 強い時間減衰を伴う消散項付き非線形波動方程式に対する解の波動的な 爆発とlifespan評価2018

    • Author(s)
      高村博之・頼宇安
    • Organizer
      2018日本数学会秋季総合分科会函数方程式論分科会, 岡山大学
    • Related Report
      2018 Annual Research Report
  • [Presentation] スケール不変な消散項をもつ1次元半線形波動方程式の解のライフスパン2018

    • Author(s)
      高村博之
    • Organizer
      八戸における偏微分方程式論集中ワークショップ 第九回北海道-東北コンソーシアムセミナー
    • Related Report
      2018 Annual Research Report
    • Invited
  • [Presentation] Multipliers on the wave-like blow-up for nonlinear damped wave equations2018

    • Author(s)
      H.Takamura
    • Organizer
      The 11th Mathematical Society of Japan (MSJ) Seasonal Institute (SI) The Role of Metrics in the Theory of Partial Differential Equations, 北海道大学
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Wave-like blow-up for semilinear damped wave equation2018

    • Author(s)
      高村博之
    • Organizer
      名古屋微分方程式セミナー, 名古屋大学
    • Related Report
      2018 Annual Research Report
    • Invited
  • [Presentation] The “wave-like” blow-up for nonlinear wave equations with the scattering damping2018

    • Author(s)
      H.Takamura
    • Organizer
      Eighth Euro-Japanese Workshop on Blow-up, 東北大学
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] 非線形消散波動方程式の波動的な解の爆発2018

    • Author(s)
      高村博之
    • Organizer
      応用解析研究会, 早稲田大学
    • Related Report
      2018 Annual Research Report
    • Invited
  • [Presentation] 非線形消散波動方程式の波動的な解の爆発2018

    • Author(s)
      高村博之
    • Organizer
      東北大学大学院理学研究科談話会
    • Related Report
      2018 Annual Research Report
    • Invited
  • [Presentation] 非線形波動方程式の解析から非線形消散波動方程式の解析へ2018

    • Author(s)
      高村博之
    • Organizer
      東北大学応用数学セミナー
    • Related Report
      2018 Annual Research Report
    • Invited
  • [Presentation] Sharp estimate of lifespan to semi linear damped wave equation with an effective time-dependent damping2018

    • Author(s)
      M.Ikeda
    • Organizer
      International Workshop on "Fundamental Problems in Mathematical and Theoretical Physics", Waseda University,
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Blow-up of solutions to semi linear wave equation with a scaling invariant critical damping2018

    • Author(s)
      M.Ikeda
    • Organizer
      MSJ-SI "The Role of Metrics in the Theory of Partial Differential Equations", Hokkaido University
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] 空間変数に依存するスケール臨界な摩擦項を持つ非線形波動方程式の小さな初期値に対する解の爆発2018

    • Author(s)
      池田正弘
    • Organizer
      南大阪セミナー, 大阪市立大学
    • Related Report
      2018 Annual Research Report
    • Invited
  • [Presentation] On a test function method for blowup of solutions to semi linear damped wave equations2018

    • Author(s)
      池田正弘, 側島基宏
    • Organizer
      2018年日本数学会秋季総合分科会, 岡山大学
    • Related Report
      2018 Annual Research Report
  • [Presentation] Weighted energy estimates for wave equation with space-dependent damping term for slowly decaying initial data2018

    • Author(s)
      Y.Wakasugi
    • Organizer
      12th AIMS Conference on Dynamical Systems, Differential Equations and Applications, SS102: Asymptotics for Nonlinear Diffusion Equations and Related Topics, National Taiwan University
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Critical exponent for the semilinear wave equation with a damping term depending on time and space variable2018

    • Author(s)
      若杉勇太
    • Organizer
      名古屋偏微分方程式研究集会, 名古屋工業大学
    • Related Report
      2018 Annual Research Report
  • [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, 名古屋大学
    • Related Report
      2018 Annual Research Report
    • Invited
  • [Presentation] On the blow-up theorem for critical semilinear wave equations2018

    • Author(s)
      K.Wakasa
    • Organizer
      16th Linear and Nonlinear Waves, 滋賀県立県民交流センター
    • Related Report
      2018 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] On the blow-up theorem for critical semilinear wave equations2018

    • Author(s)
      若狭恭平
    • Organizer
      名古屋偏微分方程式研究集会,名古屋工業大学
    • Related Report
      2018 Annual Research Report
  • [Presentation] On the blow-up theorem for critical semilinear wave equations2018

    • Author(s)
      若狭恭平
    • Organizer
      三重における非線形波動方程式研究集会, 三重大学
    • Related Report
      2018 Annual Research Report
    • Invited
  • [Funded Workshop] 第20回北東数学解析研究会, 東北大学2019

    • Related Report
      2018 Annual Research Report

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Published: 2018-04-23   Modified: 2021-12-27  

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