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Asymptotic Analysis of quasilinear ordinary differential equations and its application to asymptotic analysis of elliptic equations

Research Project

Project/Area Number 23540196
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Basic analysis
Research InstitutionGifu University

Principal Investigator

USAMI Hiroyuki  岐阜大学, 工学部, 教授 (90192509)

Co-Investigator(Renkei-kenkyūsha) NAITO Manabu  愛媛大学, 大学院理工学研究科, 教授 (00106791)
KAMO Ken-ichi  札幌医科大学, 医療人育成センター, 准教授 (10404740)
TANIGAWA Tomoyuki  熊本大学, 教育学部, 准教授 (10332008)
TERAMOTO Tomomitsu  尾道大学, 経済情報学部, 助教 (20398465)
Project Period (FY) 2011-04-28 – 2015-03-31
Project Status Completed (Fiscal Year 2014)
Budget Amount *help
¥3,120,000 (Direct Cost: ¥2,400,000、Indirect Cost: ¥720,000)
Fiscal Year 2014: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2013: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2012: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2011: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Keywords常微分方程式 / 漸近挙動 / 波動方程式 / 逆問題 / 準線形 / 解の爆発 / フーリエ解析 / 漸近解析 / Karamata関数 / 楕円型方程式 / 競争系
Outline of Final Research Achievements

(1) We found the asymptotic forms of solutions of quasilinear ordinary differential equations. In particular, we found asymptotic behavior of positive solutions belonging to classes of Karamata functions under considerably weak assumptions. We could also find existence results for so-called intermediate growth solutions. Finally, we could solve inverse problems concerning to blow-up times.
(2) We could analyze linear hyperbolic equations with damping terms based on Fourier Analysis. In order to examine asymptotic behavior of solutions of reaction-diffusion systems, we analyzed Lanchester type ordinary differential systems. We found that, as in the classical systems, there are critical values for initial data classifying asymptotic behavior of solutions essentially.

Report

(5 results)
  • 2014 Annual Research Report   Final Research Report ( PDF )
  • 2013 Research-status Report
  • 2012 Research-status Report
  • 2011 Research-status Report
  • Research Products

    (21 results)

All 2015 2014 2013 2012 2011 Other

All Journal Article (10 results) (of which Peer Reviewed: 9 results,  Acknowledgement Compliant: 1 results) Presentation (11 results) (of which Invited: 1 results)

  • [Journal Article] Determination of a nonlinearity from blow-up time2014

    • Author(s)
      Y. Kamimura and H. Usami
    • Journal Title

      Proc. Japan Acad. Ser A

      Volume: 90 Pages: 127-132

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Asymptotic analysis of positive solutions of third order nonlinear differential equations2014

    • Author(s)
      J. Jaros, T. Kusano and T. Tanigawa
    • Journal Title

      Hiroshima Math. J.

      Volume: 44 Pages: 1-34

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed
  • [Journal Article] 逆爆発時刻問題2013

    • Author(s)
      宇佐美広介,上村豊
    • Journal Title

      日本数学会 秋季総合分科会 函数方程式論分科会アブストラクト

      Volume: なし Pages: 36-37

    • Related Report
      2013 Research-status Report
  • [Journal Article] A remark on the existence of slowly growing positive solutions to second order super-linear ordinary differential equations2013

    • Author(s)
      Manabu Naito
    • Journal Title

      Nonlinear Differential Equations and Applications

      Volume: 20 Pages: 1759-1769

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] Asymptotic analysis of positive solutions of third order nonlinear differential equations in the framework of regular variation2013

    • Author(s)
      Jaroslav Jaros, Takasi Kusano, and Tomoyuki Tanigawa
    • Journal Title

      Mathematische Nachrichten

      Volume: 296 Pages: 205-223

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] Rectifiable oscillations of radially symmetric solutions of p-Laplace differential equations2012

    • Author(s)
      Y. Naito, M. Pasic, and H. Usami
    • Journal Title

      Differential Equations and Applications

      Volume: 4 Pages: 11-25

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] Existence of solutions of integral equations related to inverse problems of quasilinear ordinary differential equations2012

    • Author(s)
      H. Usami, and Y. Takuro
    • Journal Title

      Mem. Differntial Equations Math. Phys.

      Volume: 57 Pages: 163-176

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] A note on the existence of slowly growing positive solutions to second order quasilinear ordinary differential equations2012

    • Author(s)
      M. Naito
    • Journal Title

      Mem. Differntial Equations Math. Phys.

      Volume: 57 Pages: 95-108

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] An asymptotic analysis of positive solutions of generalized Thomas-Fermi differntial equations2012

    • Author(s)
      T. Kusano, V. Maric, and T. Tanigawa
    • Journal Title

      Nonlinear Anal.

      Volume: 75 Pages: 2474-2485

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] Rectifiable oscillations of radially symmetric solutions of p-Laplace differential equations2011

    • Author(s)
      Yuki Naito, mervan pasic, and Hiroyuki Usami
    • Journal Title

      Differential Equations and Applications

      Volume: 印刷中

    • Related Report
      2011 Research-status Report
    • Peer Reviewed
  • [Presentation] ある Lanchester 型モデルの解の漸近挙動2015

    • Author(s)
      宇佐美広介, チャン ティ フェン チャン
    • Organizer
      日本数学会年会
    • Place of Presentation
      明治大学(東京都)
    • Year and Date
      2015-03-21
    • Related Report
      2014 Annual Research Report
  • [Presentation] 逆爆発問題の大域解2014

    • Author(s)
      上村豊,宇佐美広介
    • Organizer
      日本数学会年会
    • Place of Presentation
      広島大学(東広島市)
    • Year and Date
      2014-09-25
    • Related Report
      2014 Annual Research Report
  • [Presentation] 常微分方程式の双曲型方程式への応用2014

    • Author(s)
      宇佐美広介
    • Organizer
      日本数学会年会
    • Place of Presentation
      広島大学(東広島市)
    • Year and Date
      2014-09-25
    • Related Report
      2014 Annual Research Report
  • [Presentation] 変数係数はどう方程式のフーリエ級数を用いた解析2014

    • Author(s)
      宇佐美広介, 髙木賢司
    • Organizer
      振動理論ワークショプーー金沢2014
    • Place of Presentation
      金沢大学
    • Related Report
      2013 Research-status Report
  • [Presentation] Existence of solutions of Integral Equations Related to Inverse Problems of Quasilinear Ordinary Differential Equations2013

    • Author(s)
      Hiroyuki Usami
    • Organizer
      Equadiff13
    • Place of Presentation
      チェコ共和国,プラハ市
    • Related Report
      2013 Research-status Report
  • [Presentation] 逆爆発時刻問題2013

    • Author(s)
      宇佐美広介,上村豊
    • Organizer
      日本数学会秋季総合分科会函数方程式論分科会
    • Place of Presentation
      愛媛大学
    • Related Report
      2013 Research-status Report
  • [Presentation] Inverse Problems for blow-up times2013

    • Author(s)
      Hiroyuki Usami
    • Organizer
      Workshop on Differential Equations in Gifu2013
    • Place of Presentation
      岐阜大学
    • Related Report
      2013 Research-status Report
  • [Presentation] Asymptotic analysis of positive decreasing solutions of a class od systems of second order nonlinear differential equations in the framework of regular variation2013

    • Author(s)
      Tomoyuki Tanigawa
    • Organizer
      Equadiff2013
    • Place of Presentation
      チェコ共和国,プラハ市
    • Related Report
      2013 Research-status Report
  • [Presentation] 2階優線形常微分方程式の弱増加正値解の存在(その2)

    • Author(s)
      内藤学
    • Organizer
      愛知教育大学における微分方程式セミナー
    • Place of Presentation
      愛知教育大学
    • Related Report
      2012 Research-status Report
  • [Presentation] Existence of solutions of integral equations related to inverse problems of quasilinear ordinary differential equations

    • Author(s)
      宇佐美広介
    • Organizer
      偏微分方程式の逆問題とその周辺に関する研究
    • Place of Presentation
      京都大学数理解析研究所
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] Global asymptotic stability in a two-species nonautonomous competition system

    • Author(s)
      宇佐美広介
    • Organizer
      京都大学数理解析研究所(招待講演)
    • Place of Presentation
      京都大学
    • Related Report
      2011 Research-status Report

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Published: 2011-08-05   Modified: 2019-07-29  

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