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2008 Fiscal Year Final Research Report

Theory of nonlocal nonlinear differential equations and optimization,and applications

Research Project

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Project/Area Number 18540178
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Basic analysis
Research InstitutionShimane University

Principal Investigator

KATO Nobuyuki  Shimane University, 総合理工学部, 教授 (40177423)

Co-Investigator(Renkei-kenkyūsha) FURUMOCHI Tetsuro  島根大学, 総合理工学部, 教授 (40039128)
KUROIWA Daishi  島根大学, 総合理工学部, 准教授 (40284020)
MACHIHARA Shuji  埼玉大学, 教育学部, 准教授 (20346373)
Project Period (FY) 2006 – 2008
Keywordsサイズ依存 / 個体数変動 / 非線形成長率 / 最適収穫問題 / 最大原理
Research Abstract

サイズ構造を持つ線形個体数変動モデルとその双対問題に対する解の存在と一意性に関する基本理論を整備するとともに最適収穫問題に対して最適制御の存在や最適制御であるための必要条件を与える最大値原理についての結果を得た。また、非線形の場合にも収穫率が時間のみに依存する場合に最適収穫率の存在を得た。一方、多種生物系をモデルとするサイズ構造を持つ一般の非線形系に対する解の存在、総個体数の有界性、および総個体数の減衰に関する結果を得た。

  • Research Products

    (9 results)

All 2008 2007 2006

All Journal Article (5 results) (of which Peer Reviewed: 5 results) Presentation (4 results)

  • [Journal Article] Maximum principle for optimal harvesting in linear size-structured population2008

    • Author(s)
      N. Kato
    • Journal Title

      Mathematical Population Studies 15

      Pages: 123-136

    • Peer Reviewed
  • [Journal Article] Optimal harvesting for nonlinear size-structured population dynamics2008

    • Author(s)
      N. Kato
    • Journal Title

      J. Math. Anal Appl. 342

      Pages: 1388-1398

    • Peer Reviewed
  • [Journal Article] A system of non-autonomous nonlinear size-structured population dynamics, Special Issue of Dynamics of Continuous2007

    • Author(s)
      N. Kato
    • Journal Title

      Discrete and Impulsive Systems Series A 14(S2)

      Pages: 79-84

    • Peer Reviewed
  • [Journal Article] Size-structured plant population models and harvesting problems2007

    • Author(s)
      N. Kato, S. Oharu and K. Shitaoka
    • Journal Title

      J. Comp Appl. Math. 204

      Pages: 114-123

    • Peer Reviewed
  • [Journal Article] Linear size-structured population models and optimal harvesting problems2006

    • Author(s)
      N. Kato
    • Journal Title

      J. Ecol Dev. Vol. 5 No. F06

      Pages: 6-19

    • Peer Reviewed
  • [Presentation] Optimal harvesting for two-system model in size-structured population2008

    • Author(s)
      N. Kato
    • Organizer
      The 5th World Congress of Nonlinear Analysts
    • Place of Presentation
      Orlando, Florida, USA
    • Year and Date
      2008-07-01
  • [Presentation] サイズ構造を持つ個体数変動方程式2008

    • Author(s)
      蚊戸宣幸
    • Organizer
      2009年度日本数学会年会実函数論分科会特別講演
    • Place of Presentation
      東京大学
    • Year and Date
      2008-03-26
  • [Presentation] A system of size-structured population dynamics with nonlinear growth rate2007

    • Author(s)
      N. Kato
    • Organizer
      Equadiff07, 2007. 8., Vienna University of Thechnology
    • Place of Presentation
      Vienna, Austria
    • Year and Date
      2007-08-01
  • [Presentation] A system of non-autonomous nonlinear size-structured population dynamics2006

    • Author(s)
      N. Kato
    • Organizer
      The 5th International Conference on Differential Equations and Dynamical Systems
    • Place of Presentation
      University of Texas-Pan American, Edinburg, Texas, USA
    • Year and Date
      2006-12-01

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Published: 2010-06-10   Modified: 2016-04-21  

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