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

Kirchhoff equation and p-Laplacian wave equation

Research Project

Project/Area Number 22540171
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Basic analysis
Research InstitutionUniversity of Tsukuba

Principal Investigator

KAJITANI Kunihiko  筑波大学, 名誉教授 (00026262)

Project Period (FY) 2010-04-01 – 2014-03-31
Project Status Completed (Fiscal Year 2013)
Budget Amount *help
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2013: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2012: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2011: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2010: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Keywordsキルヒホフ方程式 / 漸近解 / 大域解 / 解の時間減衰 / 混合問題 / 熱方程式 / 強ロパチンスキ条件 / 時間減衰評価 / ストークス方程式 / ノントラッピング条件 / 解の漸近挙動 / 熱方程式の一般境界値問題 / L^p-L^q 評価 / 可積分条件 / 時間大域解 / L^p評価 / p-ラプラシアン / p-ラプラシアン方程式 / 境界値問題
Research Abstract

1.The fundamental solutions of the mixed problem with the single and general bo undary conditions have the L1-L\infty and Lp boundedness, if and only if the bo undary operator satisfies the strong Lopatinski conditions and the alpha condit ion. Moreover if we assume only the strong Lopatinski conditins without the alp ha condition, we can get the Lp boundednss of solutions for 1<p<infty. which ar e proved in: Kajitani and Baba: Time decay estimates of solutions to the mixed problem for heat equtions in a half space, Tsukuba J. Math.(2013).
2.The time global solutions an the time asymptotic solutions to the Cauchy prob lem of the perturbed Kirhhoff equations in the hall space was obtained under th e conditions that the nitial data satisfy some integral conditions with respect to the time and thecoefficients satisfy nontrapping conditions.

Report

(5 results)
  • 2013 Annual Research Report   Final Research Report ( PDF )
  • 2012 Annual Research Report
  • 2011 Annual Research Report
  • 2010 Annual Research Report
  • Research Products

    (34 results)

All 2014 2013 2012 2011 2010

All Journal Article (5 results) (of which Peer Reviewed: 5 results) Presentation (29 results) (of which Invited: 25 results)

  • [Journal Article] Time decay estimates of solutions to the mixed problem for heat equations in a half space2013

    • Author(s)
      T. A. Baba and K. Kajitani
    • Journal Title

      Tsukuba J. Math.

      Volume: Vol.37 Pages: 271-305

    • NAID

      120006582877

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Time decay estimates of solutions to mixed problem for the heat equations in a half space2013

    • Author(s)
      Kajitani and Baba
    • Journal Title

      Tsukuba Journal of Mathematics

      Volume: 37 Pages: 271-305

    • NAID

      120006582877

    • Related Report
      2013 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Asymptotic behaviors for multi- dimensional perturbed Kirchhoff equations2012

    • Author(s)
      K. Kajitani
    • Journal Title

      Tsukuba J. Math.

      Volume: Vol.36 Pages: 1-42

    • Related Report
      2013 Final Research Report
    • Peer Reviewed
  • [Journal Article] Asymptotic behaviors for multidimensiional Kirhhoff equations2012

    • Author(s)
      Kunihiko Kajitani
    • Journal Title

      Tsukuba Journal of Mathematics

      Volume: 36 Pages: 1-42

    • Related Report
      2012 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Asymptotic behaviors of solutions multidimensional Kirchhoff equations2012

    • Author(s)
      Kunihiko Kajitani
    • Journal Title

      Tsukuba Journal of mathematics

      Volume: 36 Pages: 1-27

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Presentation] ストース方程式の混合問題の解のLp有界性2014

    • Author(s)
      K. Kajitani
    • Organizer
      早稲田大学応用解析研究会
    • Place of Presentation
      箱根湯本
    • Year and Date
      2014-03-10
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] ストース方程式の混合問題の解のグラヂエントのLp有界性2014

    • Author(s)
      K. Kajitani
    • Organizer
      松山キャンプ
    • Place of Presentation
      山口大学
    • Year and Date
      2014-01-05
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] ストークス方程式の混合問題の時間減衰現象2014

    • Author(s)
      梶谷邦彦
    • Organizer
      松山キャンプ
    • Place of Presentation
      山口大学
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] ストークス方程式の混合問題の時間減衰現象2014

    • Author(s)
      梶谷邦彦
    • Organizer
      梶谷邦彦
    • Place of Presentation
      箱根湯本
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] ストース方程式の混合問題の解のグラヂエントのLp有界性2013

    • Author(s)
      K. Kajitani
    • Organizer
      パリ6大学解析セミナー
    • Place of Presentation
      パリ、ポアンカレ研究所
    • Year and Date
      2013-12-19
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] ストークス方程式の混合問題に対する解の減衰評価2013

    • Author(s)
      K. Kajitani
    • Organizer
      第20回超局所解析と古典解析
    • Place of Presentation
      京都大学
    • Year and Date
      2013-11-21
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] 熱方程式の境界値問題の時間減衰現象2013

    • Author(s)
      K. Kajitani
    • Organizer
      京都産業大学解析セミナー
    • Place of Presentation
      京都産業大学
    • Year and Date
      2013-09-06
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] ストークス方程式の混合問題に対する解のグラヂエントの減衰評価2013

    • Author(s)
      K. Kajitani
    • Organizer
      早稲田大学応用解析研究会
    • Place of Presentation
      湯河原
    • Year and Date
      2013-03-02
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] ストークス方程式の混合問題に対する解のグラヂエントのLp評価2013

    • Author(s)
      K. Kajitani
    • Organizer
      松山キャンプ
    • Place of Presentation
      山口大学
    • Year and Date
      2013-01-05
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] ストークス方程式の混合問題の解表示2013

    • Author(s)
      梶谷邦彦
    • Organizer
      数理現象における多様の解析的アプローチn研究会
    • Place of Presentation
      京都産業大学
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] ストークス方程式の混合問題の時間減衰現象2013

    • Author(s)
      梶谷邦彦
    • Organizer
      ポアンカレ研究所解析セミナー
    • Place of Presentation
      フランスパリポアンカレ研究所
    • Related Report
      2013 Annual Research Report
    • Invited
  • [Presentation] ストークス方程式に対する混合問題の解の時間減衰2013

    • Author(s)
      梶谷邦彦
    • Organizer
      第20回早稲田大学応用解析研究会シンポジイウム
    • Place of Presentation
      湯河原温泉ホテルあかね(神奈川県)
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] 熱方程式の混合問題の解のL^1 と L^inftyにおける有界性2013

    • Author(s)
      梶谷邦彦
    • Organizer
      松山キャンプ
    • Place of Presentation
      山口大学(山口県)
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] ストークス方程式の混合問題に対する解のLp評価2012

    • Author(s)
      K. Kajitani
    • Organizer
      パリ6大学解析セミナー
    • Place of Presentation
      パリポアンカレ研究所
    • Year and Date
      2012-12-17
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] 半空間における熱方程式の混合問題の時間減衰現象2012

    • Author(s)
      K. Kajitani
    • Organizer
      夏の作用素論シンポジウム
    • Place of Presentation
      新潟大学
    • Year and Date
      2012-09-07
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] Lp boundedness of solutions to mixed problem for the heat equation2012

    • Author(s)
      K. Kajitani
    • Organizer
      上見先生追悼研究会
    • Place of Presentation
      北海道大学
    • Year and Date
      2012-08-24
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] 熱方程式の混合問題に対する解の減衰評価2012

    • Author(s)
      K. Kajitani
    • Organizer
      早稲田大学応用解析研究会
    • Place of Presentation
      熱海
    • Year and Date
      2012-03-01
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] 熱方程式に対する混合問題の解のL_p評価2012

    • Author(s)
      K. Kajitani
    • Organizer
      松山キャンプ
    • Place of Presentation
      山口大学
    • Year and Date
      2012-01-05
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] L^1 and L^infty estimates of solutions for mixed problem of heat equation2012

    • Author(s)
      梶谷邦彦
    • Organizer
      Seminar of analysis of University of Paris 6
    • Place of Presentation
      ポアンカレ研究所(フランス)
    • Related Report
      2012 Annual Research Report
    • Invited
  • [Presentation] Mixed problem for the heat equation2011

    • Author(s)
      K. Kajitani
    • Organizer
      パリ6大学解析セミナー
    • Place of Presentation
      パリポアンカレ研究所
    • Year and Date
      2011-12-07
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] L^p-estimates of solutions to mixed problem of heat equations in a half space2011

    • Author(s)
      Kunihiko Kajitani
    • Organizer
      Seminar of analysis in University of Paris 6
    • Place of Presentation
      ポアンカレ研究所(フランス パリ)(招待講演)
    • Year and Date
      2011-12-07
    • Related Report
      2011 Annual Research Report
  • [Presentation] 熱方程式に対する混合問題2011

    • Author(s)
      K. Kajitani
    • Organizer
      松本作用素論セミナー
    • Place of Presentation
      信州大学
    • Year and Date
      2011-09-07
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] L_p estimates of solutions to the mixed problem for the heat equation2011

    • Author(s)
      K. Kajitani
    • Place of Presentation
      東海大学
    • Year and Date
      2011-03-11
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] L^p boundedness of solutions for mixed problem for heat eguations in a half space2011

    • Author(s)
      梶谷邦彦
    • Organizer
      発展方程式シンポジウム
    • Place of Presentation
      東海大学理学部 招待講演
    • Year and Date
      2011-03-10
    • Related Report
      2010 Annual Research Report
  • [Presentation] Mixed problem for the heat equation2011

    • Author(s)
      K. Kajitani
    • Organizer
      東海大学解析シンポジュム
    • Place of Presentation
      早稲田大学応用解析湯河原セミナー
    • Year and Date
      2011-03-02
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] Lp estimates of solutions to mixed problem for heat equations2010

    • Author(s)
      K. Kajitani
    • Organizer
      パリ6大学解析セミナー
    • Place of Presentation
      パリポアンカレ研究所
    • Year and Date
      2010-12-17
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] L^p estimates of solutions of mixed problem for heat equation in a Half space2010

    • Author(s)
      梶谷邦彦
    • Organizer
      パリ第6大学解析セミナー
    • Place of Presentation
      フランス パリポアンカレ研究所 招待講演
    • Year and Date
      2010-12-15
    • Related Report
      2010 Annual Research Report
  • [Presentation] Lp-Lq estimates of solutions to the mixed problem for the heat equation in half space2010

    • Author(s)
      K. Kajitani
    • Organizer
      ISAC国際学会
    • Place of Presentation
      ドイツドレスデン工科大学
    • Year and Date
      2010-05-26
    • Related Report
      2013 Final Research Report
    • Invited
  • [Presentation] L^p-Lq^q estimates of solutions to the mixed problem for heat equations2010

    • Author(s)
      梶谷邦彦
    • Organizer
      8th AIMS International Conferenceon Dynamical Syatems, Differeatial Equations and Applications
    • Place of Presentation
      Dresden University of Technology, Dresden, Germany
    • Year and Date
      2010-05-26
    • Related Report
      2010 Annual Research Report

URL: 

Published: 2010-08-23   Modified: 2019-07-29  

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi