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Structure on the Set of Stationary Solutions for a Two Competing Species Model with Density-Dependent Diffusion

Research Project

Project/Area Number 22540138
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field General mathematics (including Probability theory/Statistical mathematics)
Research InstitutionEhime University

Principal Investigator

KAN-ON Yukio  愛媛大学, 教育学部, 教授 (00177776)

Co-Investigator(Kenkyū-buntansha) YANAGI Shigenori  愛媛大学, 理工学研究科, 准教授 (10253296)
KADOWAKI Mitsuteru  愛媛大学, 理工学研究科, 准教授 (70300548)
Project Period (FY) 2010 – 2012
Project Status Completed (Fiscal Year 2012)
Budget Amount *help
¥4,030,000 (Direct Cost: ¥3,100,000、Indirect Cost: ¥930,000)
Fiscal Year 2012: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2011: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2010: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Keywords応用数学 / 数理モデル / 2種競争系 / 定常解の解構造 / 比較定理 / 2種競争系 / 解構造 / 数値的検証
Research Abstract

In this research, we study the structure on the set of radially symmetric positive stationary solutions for a two competing species model with density-dependent diffusion, when the habitat of the community is the inside of a ball. Although the dimension of the habitat is an integer, we assume that it can be any real number. To establish the structure, we focus on the case where the diffusion rate of the species is positive and sufficiently small, employ the bifurcation theory and the comparison principle, and then investigate the property of eigenvalues and their corresponding eigenfunctions for the linearized operator around the stationary solution.

Report

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

    (17 results)

All 2012 2011 2010 Other

All Journal Article (5 results) (of which Peer Reviewed: 5 results) Presentation (12 results)

  • [Journal Article] A note on bifurcation structure of radially symmetric stationary solutions for a reactiondiffusion system III2011

    • Author(s)
      Yukio Kan-on
    • Journal Title

      Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal.

      Volume: 18no. 5 Pages: 559-568

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] On scattering for wave equations with dissipative terms in layered media2011

    • Author(s)
      Mitsuteru Kadowaki, Hideo Nakazawa and Kazuo Watanabe
    • Journal Title

      Electron. J. Diff.Equ.

      Volume: 2011 No. 65 Pages: 1-18

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Journal Article] A note on bifurcation structure of radially symmetric stationary solutions for a reaction-diffusion system III2011

    • Author(s)
      Yukio Kan-on
    • Journal Title

      Dyn.Contin.Discrete Impuls.Syst.Ser.A Math.Anal.

      Volume: 18 Pages: 559-568

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Scattering for wave equations with dissipative terms in layered media2011

    • Author(s)
      Mitsuteru Kadowaki, Hideo Nakazawa, Kazuo Watanabe
    • Journal Title

      Electron.J.Differential Equations

      Volume: 2011 Pages: 1-18

    • Related Report
      2011 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A note on bifurcation structure of radially symmetric stationary solutions for a reactiondiffusion system II2010

    • Author(s)
      Yukio Kan-on
    • Journal Title

      Dyn. Contin. Discrete Impuls. Syst. Ser. A Math. Anal.

      Volume: 17 no. 2 Pages: 263-273

    • Related Report
      2012 Final Research Report
    • Peer Reviewed
  • [Presentation] レイリー波に対するグリーン関数について2012

    • Author(s)
      門脇光輝
    • Organizer
      夏の作用素論シンポジウム 2012
    • Place of Presentation
      新潟大学南キャンパス
    • Year and Date
      2012-09-10
    • Related Report
      2012 Final Research Report
  • [Presentation] Bifurcation structure of radially symmetric positive stationary solutions for a competition-diffusion system2012

    • Author(s)
      Yukio Kan-on
    • Organizer
      The 9th AIMS Conference on Dynamical Systems, Differential Equations and Applications
    • Place of Presentation
      Hyatt Grand Cypress Resort, Orlando, Florida, USA
    • Year and Date
      2012-07-05
    • Related Report
      2012 Final Research Report
  • [Presentation] 2種競争系の球対称全域解について2011

    • Author(s)
      観音幸雄
    • Organizer
      2011 年度秋季総合分科会応用数学分科会
    • Place of Presentation
      信州大学松本キャンパス
    • Year and Date
      2011-09-30
    • Related Report
      2012 Final Research Report
  • [Presentation] 2種競争系の球対称全域解について2011

    • Author(s)
      観音幸雄
    • Organizer
      2011日本数学会秋季総合分科会
    • Place of Presentation
      信州大学松本キャンパス
    • Year and Date
      2011-09-30
    • Related Report
      2011 Annual Research Report
  • [Presentation] On the bifurcation structure of radially symmetric positive stationary solutions for a competition-diffusion system2011

    • Author(s)
      Yukio Kan-on
    • Organizer
      The 4th MSJ-SI, Nonlinear Dynamics in Partial Differential Equations
    • Place of Presentation
      Centennial Hall, Kyushu University School of Medicine
    • Year and Date
      2011-09-14
    • Related Report
      2012 Final Research Report
  • [Presentation] On the bifurcation structure of radially symmetric positive stationary solutions for a competition-diffusion system2011

    • Author(s)
      Yukio Kan-on
    • Organizer
      The 4th MSJ-SI, Nonlinear Dynamics in Partial Differential Equations
    • Place of Presentation
      九州大学医学部百年講堂
    • Year and Date
      2011-09-14
    • Related Report
      2011 Annual Research Report
  • [Presentation] 3次元半空間の波動伝播と定常位相の方法について2011

    • Author(s)
      門脇光輝
    • Organizer
      広島数理解析セミナー
    • Place of Presentation
      広島大学西条キャンパス
    • Year and Date
      2011-05-27
    • Related Report
      2011 Annual Research Report
  • [Presentation] 3次元半空間の波動伝播と定常位相の方法について2011

    • Author(s)
      門脇光輝
    • Organizer
      解析セミナー
    • Place of Presentation
      愛媛大学城北キャンパス
    • Year and Date
      2011-04-22
    • Related Report
      2012 Final Research Report
  • [Presentation] Yafaev の定式化による散乱理論2010

    • Author(s)
      門脇光輝
    • Organizer
      新潟偏微分方程式研究集会
    • Place of Presentation
      新潟大学南キャンパス
    • Year and Date
      2010-10-10
    • Related Report
      2012 Final Research Report
  • [Presentation] Yafaevの定式化による散乱理論2010

    • Author(s)
      門脇光輝
    • Organizer
      新潟偏微分方程式研究集会
    • Place of Presentation
      新潟大学南キャンパス
    • Year and Date
      2010-10-10
    • Related Report
      2010 Annual Research Report
  • [Presentation] Bifurcation structure of radially symmetric positive stationary solutions for a competition-diffusion system

    • Author(s)
      Yukio Kan-on
    • Organizer
      The 9th AIMS Conference on Dynamical Systems, Differential Equations and Applications
    • Place of Presentation
      Hyatt Regency Grand Cypress (Orlando, USA)
    • Related Report
      2012 Annual Research Report
  • [Presentation] レイリー波に対するグリーン関数について

    • Author(s)
      門脇 光輝
    • Organizer
      夏の作用素論シンポジウム2012
    • Place of Presentation
      新潟大学南キャンパス
    • Related Report
      2012 Annual Research Report

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

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