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Unified investigation on elliptic and parabolic equations

Research Project

Project/Area Number 23540248
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Global analysis
Research InstitutionOsaka Prefecture University

Principal Investigator

KABEYA Yoshitsugu  大阪府立大学, 工学(系)研究科(研究院), 教授 (70252757)

Co-Investigator(Renkei-kenkyūsha) ISHIGE Kazuhiro  東北大学, 理学研究科, 教授 (90272020)
Project Period (FY) 2011-04-28 – 2015-03-31
Project Status Completed (Fiscal Year 2014)
Budget Amount *help
¥4,810,000 (Direct Cost: ¥3,700,000、Indirect Cost: ¥1,110,000)
Fiscal Year 2014: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2013: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2012: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2011: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Keywordsホットスポット / 楕円型方程式 / 放物型方程式 / 時間大域挙動 / 時間減衰 / シュレディンガー半群 / 時間大域的挙動 / 固有値 / 重心 / 臨界作用素 / 劣臨界作用素 / 正値定常解 / 劣臨界シュレディンガー半群 / 熱方程式 / 楕円型偏微分方程式 / 構造定理
Outline of Final Research Achievements

With Professor Kazuhiro Ishige, who is my liaison collabolator, I investigated the large time behaviors of solutions to linear parabolic equations. During the research, I found that properties of a positive solution to the corresponding elliptic equations, which describe the steady states, affect the large time behaviors of solutions and published the main results in Journal of Functional analysis in 2012. Also related results on large time behaviors of solutions were
published in foreign academic journals.
Properties of solutions to elliptic equations on a sphere or on the hyperbolic space were also invesitgated and published in foreign academic journals.

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

    (28 results)

All 2014 2013 2012 2011 Other

All Journal Article (7 results) (of which Peer Reviewed: 7 results,  Acknowledgement Compliant: 1 results) Presentation (19 results) (of which Invited: 13 results) Remarks (2 results)

  • [Journal Article] Eigenvalues of the Lapace-Beltrami operator on a large spherical cap under the Robin condition2014

    • Author(s)
      Yoshitsugu Kabeya, Tatsuki Kawakami, Atsushi Kosaka, Hirokazu Ninomiya
    • Journal Title

      Kodai Mathematical Journal

      Volume: 37 Pages: 620-645

    • Related Report
      2014 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Existence and uniqueness of singular solutions for elliptic equation on the hyperbolic space2014

    • Author(s)
      Yen-Lin Wu, Chi-You Chen, Jann-Long Chern, Yoshitsugu Kabeya
    • Journal Title

      Communications on Pure and Applied Analysis

      Volume: 13 Issue: 2 Pages: 949-960

    • DOI

      10.3934/cpaa.2014.13.949

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] A unified approach to Matukuma type equations on the hyperbolic space or on a sphere2013

    • Author(s)
      Yoshitsugu Kabeya
    • Journal Title

      Discrete and Continuous Dynamical Systems, Supplement

      Volume: 1 Pages: 385-391

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] A Unified Approach to Matukuma Type Equations on the Hyperbolic Space or on a Sphere2013

    • Author(s)
      Yoshitsugu Kabeya
    • Journal Title

      Proceedings of AIMS Conference

      Volume: 未定

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] Decay rate of L^q norms of critical Schrodinger heat semigroups2013

    • Author(s)
      Kazuhiro Ishige and Yoshitsugu Kabeya
    • Journal Title

      Geometric Properties of Elliptic and Parabolic PDE's, Springer INdAM Series

      Volume: 2 Pages: 165-178

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Journal Article] L^p norms of nonnegative Schroedinger heat semigroup and the large time behavior of hot spots2012

    • Author(s)
      K. Ishige and Y. Kabeya
    • Journal Title

      J. Funct. Anal.

      Volume: 262 Issue: 6 Pages: 2695-2733

    • DOI

      10.1016/j.jfa.2011.12.024

    • Related Report
      2011 Research-status Report
    • Peer Reviewed
  • [Journal Article] On the positive, ``radial" solutions of a semilinear elliptic equation in H^N2012

    • Author(s)
      Catherine Bandle, Yoshitsugu Kabeya
    • Journal Title

      Advances in Nonlinear Analysis

      Volume: 1 Issue: 1 Pages: 1-25

    • DOI

      10.1515/ana-2011-0004

    • Related Report
      2011 Research-status Report
    • Peer Reviewed
  • [Presentation] 球面上での領域のラプラス・ベルトラミ作用素と関連する非線形問題2014

    • Author(s)
      壁谷 喜継
    • Organizer
      大阪大学情報学研究科第11回情報数理学セミナー
    • Place of Presentation
      大阪大学大学院情報学研究科,吹田市
    • Year and Date
      2014-11-27
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] 球面上での領域のラプラス・ベルトラミ作用素と関連する非線形問題2014

    • Author(s)
      壁谷 喜継
    • Organizer
      数学と現象(Mathematics and Phenomena) in Miyazaki 2014
    • Place of Presentation
      宮崎大学,宮崎市
    • Year and Date
      2014-11-14 – 2014-11-15
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] Solutions to the equation of the scalar-field type on a large spherical cap2014

    • Author(s)
      Yoshitsugu Kabeya
    • Organizer
      京都大学数理解析研究所研究集会
    • Place of Presentation
      京都大学数理解析研究所,京都市
    • Year and Date
      2014-11-05 – 2014-11-07
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] Eigenvalues of the Laplace-Beltrami operator on a spherical cap and related topics2014

    • Author(s)
      Yoshitsugu Kabeya
    • Organizer
      International Symposium on Applied Analysis
    • Place of Presentation
      University of Zurich, Zurich, Switzerland
    • Year and Date
      2014-06-11 – 2014-06-12
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] 球面でのラプラス・ベルトラミ作用素と関連する非線形問題2014

    • Author(s)
      壁谷 喜継
    • Organizer
      九州函数方程式セミナー
    • Place of Presentation
      福岡大学セミナーハウス,福岡市
    • Year and Date
      2014-05-30
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] Eigenvalues of the Laplace-Beltrami operator on a spherical cap and related nonlinear problems2014

    • Author(s)
      壁谷 喜継
    • Organizer
      名古屋大学微分方程式セミナー
    • Place of Presentation
      名古屋大学多元数理研究科,名古屋市
    • Year and Date
      2014-05-19
    • Related Report
      2014 Annual Research Report
    • Invited
  • [Presentation] Bifurcation diagrams of a nonlinear eplliptic problem on a spherical cap2013

    • Author(s)
      Yoshitsugu Kabeya
    • Organizer
      International Workshop on Stationary Problems in Nonlinear Partial Differential Equations
    • Place of Presentation
      佐賀大学
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] Unified approach to Matukuma type equations on the hyperbolic space or on a sphere2012

    • Author(s)
      Yoshitsugu Kabeya
    • Organizer
      10th AIMS conference on Differential Equations
    • Place of Presentation
      Orlando, FL, USA
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] Bifurcation diagrams of nonlinear elliptic problems on a spherical cap2012

    • Author(s)
      Yoshitsugu Kabeya
    • Organizer
      3rd Swiss-Japanese Seminar
    • Place of Presentation
      Zurich, Switzerland
    • Related Report
      2012 Research-status Report
    • Invited
  • [Presentation] Structures of positive solutions to nonlinear elliptic problems on the hyperbolic space or on a spherical cap2012

    • Author(s)
      Yoshitsugu Kabeya
    • Organizer
      第29回九州における偏微分方程式集会(招待講演)
    • Place of Presentation
      九州大学
    • Related Report
      2011 Research-status Report
  • [Presentation] Structure of nonlinear elliptic equations on manifolds2011

    • Author(s)
      Yoshitsugu Kabeya
    • Organizer
      Korea-Japan international wrokshop on PDE(招待講演)
    • Place of Presentation
      釜山大学
    • Related Report
      2011 Research-status Report
  • [Presentation] 楕円型偏微分方程式に対する球対称解の構造2011

    • Author(s)
      壁谷 喜継
    • Organizer
      日本数学会(招待講演)
    • Place of Presentation
      信州大学
    • Related Report
      2011 Research-status Report
  • [Presentation] Large time behaviors of hot spots of solutions to a linear heat equation2011

    • Author(s)
      Yoshitsugu Kabeya
    • Organizer
      International Workshop on Modeling and Analysis of PDE Systems of Biological Processess(招待講演)
    • Place of Presentation
      北京首都師範大学
    • Related Report
      2011 Research-status Report
  • [Presentation] Decay Estimates to a Linear Heat Equation with a Potential and Related Topics2011

    • Author(s)
      Yoshitsugu Kabeya
    • Organizer
      2011 NCTS Taiwan-Japan Joint Workshop on PDEs and Geometric Analysis(招待講演)
    • Place of Presentation
      台湾国家理論科学中心
    • Related Report
      2011 Research-status Report
  • [Presentation] Non-azimuthal solutions to a nonlinear elliptic equation on a spherical cap

    • Author(s)
      Yoshitsugu Kabeya
    • Organizer
      2013 Workshop in Nonlinear Equations in Population Biology
    • Place of Presentation
      華東師範大学 (中国)
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] A unified approach to nonlinear elliptic problems on the hyperbolic space or on the sphere

    • Author(s)
      Yoshitsugu Kabeya
    • Organizer
      Applied Mathematics Seminar
    • Place of Presentation
      University of Zurich (スイス)
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] Bifurcation diagrams of the nonlinear elliptic equation of the scalar-filed type on a spherical cap

    • Author(s)
      Yoshitsugu Kabeya
    • Organizer
      20th Microlocal Analysis and Classical Analysis
    • Place of Presentation
      京都大学
    • Related Report
      2013 Research-status Report
  • [Presentation] Bifurcation diagrams of a nonlinear elliptic equation on a spherical cap

    • Author(s)
      Yoshitsugu Kabeya
    • Organizer
      NTU and NCTS/TPE seminar on PDE
    • Place of Presentation
      台湾大学(台湾)
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] Bifurcation diagrams of a nonlinear elliptic equation on a spherical cap

    • Author(s)
      Yoshitsugu Kabeya
    • Organizer
      PDE Seminar
    • Place of Presentation
      國立中央大学(台湾)
    • Related Report
      2013 Research-status Report
    • Invited
  • [Remarks] 壁谷喜継のサイト

    • URL

      http://www.ms.osakafu-u.ac.jp/~kabeya

    • Related Report
      2014 Annual Research Report
  • [Remarks] 教員活動情報データベース

    • URL

      http://kyoindb.acs.osakafu-u.ac.jp/profile/out.zJYV.5Ulg9rtFmpexb38bA==.html

    • Related Report
      2013 Research-status Report

URL: 

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

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