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Mathematical analysis for phenomena in the living body and its simulation

Research Project

Project/Area Number 18540152
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 InstitutionFujita Health University (2008)
Fujita Health University College (2006-2007)

Principal Investigator

HOSHINO Hiroki  Fujita Health University, 医療科学部, 准教授 (80238740)

Co-Investigator(Kenkyū-buntansha) HOSONO Yuzo  京都産業大学, 理学部, 教授 (50008877)
IIDA Masato  宮崎大学, 工学部, 教授 (00242264)
ISHII Katsuyuki  神戸大学, 海事科学部, 准教授 (40232227)
内藤 守啓  藤田保健衛生大学短期大学, 衛生技術科, 准教授 (80132257)
KUBO Akisato  藤田保健衛生大学, 医療科学部, 教授 (60170023)
Co-Investigator(Renkei-kenkyūsha) HOSONO Yuzo  京都産業大学, 理学部, 教授 (50008877)
IIDA Masato  宮崎大学, 工学部, 教授 (00242264)
ISHII Katsuyuki  神戸大学, 海事科学部, 准教授 (40232227)
NAITO Morihiro  藤田保健衛生大学短期大学, 衛生技術科, 准教授 (80132257)
KUBO Akisato  藤田保健衛生大学, 医療科学部, 教授 (60170023)
Project Period (FY) 2006 – 2008
Project Status Completed (Fiscal Year 2008)
Budget Amount *help
¥3,930,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥630,000)
Fiscal Year 2008: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2007: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
Fiscal Year 2006: ¥1,200,000 (Direct Cost: ¥1,200,000)
Keywords数理モデル / 非線形現象 / 浸潤 / 進行波 / 相平面解析 / 数値シミュレーション / 反応拡散系 / 数理医学 / シミュレーション
Research Abstract

生体現象、特に悪性腫瘍細胞の結合組織への浸潤を記述した数学モデルに対する理論解析および数値シミュレーションを行った。これまで数値計算的にさまざまな進行波解が得られていたが、今回の研究において、滑らかな進行波解の存在に対する解析的な証明を与えるとともに漸近的性質を調べた。また広い意味での生命現象の数理解析を目指し、侵入現象に対する進行波解や競争系に対する解の遷移層などのパターン形成の解明を行った。

Report

(4 results)
  • 2008 Annual Research Report   Final Research Report ( PDF )
  • 2007 Annual Research Report
  • 2006 Annual Research Report
  • Research Products

    (32 results)

All 2009 2008 2007 2006

All Journal Article (14 results) (of which Peer Reviewed: 9 results) Presentation (17 results) Book (1 results)

  • [Journal Article] Traveling wave solutions to a malignant tumor invasion model2009

    • Author(s)
      H. Hoshino
    • Journal Title

      RIMS Kokyuroku 「Theory of Bio-Mathematics and Its Applications」 (to appear)

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Relative compactness in L^p of solutions of some 2m components competition-diffusion systems2008

    • Author(s)
      D. Hilhorst, M. Iida, M. Mimura and H. Ninomiya
    • Journal Title

      Discrete and Continuous Dynamical Systems Vol.21, No.1

      Pages: 233-244

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] 感染症の伝播を視る2008

    • Author(s)
      細野 雄三
    • Journal Title

      数理科学 535

      Pages: 34-38

    • Related Report
      2007 Annual Research Report
  • [Journal Article] Phase plane analysis of travelling waves for higher order autocatalytic reaction-diffusion systems, Discrete Contin2007

    • Author(s)
      Y. Hosono
    • Journal Title

      Dyn. Syst. Ser. B Vol.8, No.1

      Pages: 115-125

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] The propagation speeds of traveling fronts for higher order autocatalytic reaction-diffusion systems, Japan J. Indust2007

    • Author(s)
      Y. Hosono
    • Journal Title

      Appl. Math. Vol.24, No.1

      Pages: 79-104

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] On certain one-dimensional elliptic systems under different growth conditions at respective infinities2007

    • Author(s)
      M. Iida, K. Nakashima and E. Yanagida
    • Journal Title

      Advanced Studies in Pure Mathematics Vol.47, No.2

      Pages: 565-572

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Optimal rate of convergence to the motion by mean curvature with a driving force2007

    • Author(s)
      K. Ishii
    • Journal Title

      Advances in Differential Equations vol.12

      Pages: 481-514

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] Mathematical models of tumour angiogenesis2007

    • Author(s)
      A. Kubo and T. Suzuki
    • Journal Title

      Journal of Computational and Applied Mathematics vol.204

      Pages: 48-55

    • Related Report
      2008 Final Research Report
    • Peer Reviewed
  • [Journal Article] On certain one-dimensional elliptic systems under different growth conditions at respective infinities2007

    • Author(s)
      M. Iida, K. Nakashima, E. Yanagida
    • Journal Title

      Advanced Studies in Pure Mathematics 47

      Pages: 565-572

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Optimal rate of convergence to the motion by mean curvature with a driving force2007

    • Author(s)
      K. Ishii
    • Journal Title

      Advances in Differential Equations 12

      Pages: 481-514

    • Related Report
      2007 Annual Research Report
    • Peer Reviewed
  • [Journal Article] 感染症の伝播を記述する決定論的モデルによる空間的な伝播速度の評価2007

    • Author(s)
      細野雄三
    • Journal Title

      京都産業大学論集, 自然科学系列 36(印刷中)

    • NAID

      110006284661

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Phase plane analysis of travelling waves for higher order autocatalytic reaction-diffusion systems2007

    • Author(s)
      Yuzo Hosono
    • Journal Title

      Discrete and Continuous Dynamical Systens Series B 8・1(印刷中)

    • Related Report
      2006 Annual Research Report
  • [Journal Article] The propagation speeds of traveling fronts for higher order autocatalytic reaction-diffusion systems2007

    • Author(s)
      Yuzo Hosono
    • Journal Title

      Journal of Industrial and Applied Mathematics 24・1(印刷中)

    • NAID

      10020152715

    • Related Report
      2006 Annual Research Report
  • [Journal Article] Optimal rate of convergence to the motion by mean curvature with a driving force2007

    • Author(s)
      Katsuyuki Ishii
    • Journal Title

      Advances in Differential Equations (印刷中)

    • Related Report
      2006 Annual Research Report
  • [Presentation] 悪性腫瘍の浸潤に関連するモデルの進行波解2009

    • Author(s)
      星野弘喜
    • Organizer
      MZセミナー
    • Place of Presentation
      宮崎大学工学部
    • Year and Date
      2009-03-05
    • Related Report
      2008 Final Research Report
  • [Presentation] 悪性腫瘍の浸潤に関連するモデルの進行波解2009

    • Author(s)
      星野弘喜
    • Organizer
      第5回生物数学の理論とその応用
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2009-01-16
    • Related Report
      2008 Final Research Report
  • [Presentation] 侵入過程に現れる進行波解について2009

    • Author(s)
      細野雄三, 李聖林, 村田宙俊
    • Organizer
      第5回生物数学の理論とその応用
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2009-01-16
    • Related Report
      2008 Final Research Report
  • [Presentation] 悪性腫瘍の浸潤に関連するモデルの進行波解2009

    • Author(s)
      星野弘喜
    • Organizer
      第5回生物数学の理論とその応用(日本数理生物学会後援)
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2009-01-16
    • Related Report
      2008 Annual Research Report
  • [Presentation] 個体群侵入における段階別侵入速度について2008

    • Author(s)
      飯田雅人
    • Organizer
      盛岡応用数学小研究集会
    • Place of Presentation
      岩手大学
    • Year and Date
      2008-12-13
    • Related Report
      2008 Final Research Report
  • [Presentation] An approximation scheme for motion by mean curvature2008

    • Author(s)
      K. Ishii
    • Organizer
      Mathematical Aspects of Image Processing and Computer Vision 2008
    • Place of Presentation
      北海道大学
    • Year and Date
      2008-11-21
    • Related Report
      2008 Final Research Report
  • [Presentation] 侵入問題と進行波解2008

    • Author(s)
      細野雄三
    • Organizer
      第18回日本数理生物学会大会企画シンポジウム「進行波理論と生物系、生態系への応用」
    • Place of Presentation
      同志社大学
    • Year and Date
      2008-09-18
    • Related Report
      2008 Final Research Report
  • [Presentation] Mathematical analysis for a tumor invasion model2008

    • Author(s)
      H. Hoshino
    • Organizer
      Hamamatsu Workshop on Nonlinear Evolution Equations 2008
    • Place of Presentation
      静岡県立森林公園森の家
    • Year and Date
      2008-08-11
    • Related Report
      2008 Final Research Report
  • [Presentation] Traveling fronts for the reaction-diffusion epidemic models with nonlinear incidence2008

    • Author(s)
      Y. Hosono
    • Organizer
      The Second China-Japan Colloquium of Mathematical Biology
    • Place of Presentation
      岡山大学
    • Year and Date
      2008-08-06
    • Related Report
      2008 Final Research Report
  • [Presentation] 生物集団の分散・移動を模する二種類の微分方程式-準線形拡散モデルと線形拡散・状態切替モデル-2008

    • Author(s)
      飯田雅人
    • Organizer
      ミニワークショップ「数理生態モデルをめぐる諸問題-Lotka-Volterra 系を中心として-」
    • Place of Presentation
      京都産業大学
    • Year and Date
      2008-02-23
    • Related Report
      2008 Final Research Report
  • [Presentation] Characterization of asymptotic solutions for a reaction- diffusion system around a corner layer2008

    • Author(s)
      飯田雅人
    • Organizer
      第25回九州における偏微分方程式研究集会
    • Place of Presentation
      九州大学
    • Year and Date
      2008-01-30
    • Related Report
      2008 Final Research Report
  • [Presentation] A mathematical model related to anti-angiogenesis2007

    • Author(s)
      H. Hoshino
    • Organizer
      The Workshop on Mathematical Modelling and Analysis of Biological Pattern Formations and the Related Topics
    • Place of Presentation
      名古屋大学
    • Year and Date
      2007-09-26
    • Related Report
      2008 Final Research Report
  • [Presentation] Traveling fronts for the reaction-diffusion epidemic models with nonlinear incidence2007

    • Author(s)
      Y. Hosono
    • Organizer
      The Workshop on Mathematical Modelling and Analysis of Biological Pattern Formations and the Related Topics
    • Place of Presentation
      名古屋大学
    • Year and Date
      2007-09-26
    • Related Report
      2008 Final Research Report
  • [Presentation] Mathematical analysis of Anderson-Chaplain model2007

    • Author(s)
      A. Kubo
    • Organizer
      The Workshop on Mathematical Modelling and Analysis of Biological Pattern Formations and the Related Topics
    • Place of Presentation
      名古屋大学
    • Year and Date
      2007-09-26
    • Related Report
      2008 Final Research Report
  • [Presentation] 腫瘍の浸潤に関連する偏微分方程式系の進行波解について2007

    • Author(s)
      星野弘喜
    • Organizer
      夏の偏微分方程式セミナー2007
    • Place of Presentation
      休暇村南阿蘇
    • Year and Date
      2007-08-11
    • Related Report
      2008 Final Research Report
  • [Presentation] 平均曲率流の近似問題について2006

    • Author(s)
      石井克幸
    • Organizer
      数学・物理・情報の交流シンポジウム
    • Place of Presentation
      奈良女子大学
    • Year and Date
      2006-12-16
    • Related Report
      2008 Final Research Report
  • [Presentation] Optimal rate of convergnece of the Allen - Cahn equation to the motion by mean curvature2006

    • Author(s)
      石井克幸
    • Organizer
      岐阜非線形セミナー
    • Place of Presentation
      岐阜大学
    • Year and Date
      2006-08-30
    • Related Report
      2008 Final Research Report
  • [Book] 「感染症の空間的な伝播を記述する数理モデル」(稲葉寿編著「感染症の数理モデル」)2008

    • Author(s)
      細野雄三
    • Publisher
      培風館
    • Related Report
      2008 Final Research Report

URL: 

Published: 2006-04-01   Modified: 2016-04-21  

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