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Study on the blowup solution and time global solution for the nonlinear drift-diffusion equation system

Research Project

Project/Area Number 24540201
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Global analysis
Research InstitutionMuroran Institute of Technology

Principal Investigator

KUROKIBA MASAKI  室蘭工業大学, 工学(系)研究科(研究院), 教授 (60291837)

Project Period (FY) 2012-04-01 – 2016-03-31
Project Status Completed (Fiscal Year 2015)
Budget Amount *help
¥5,200,000 (Direct Cost: ¥4,000,000、Indirect Cost: ¥1,200,000)
Fiscal Year 2015: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2014: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2013: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2012: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Keywords非線形移流拡散方程式系 / 有限時間爆発解 / 多成分系 / エントロピー / シャノンの不等式 / 初期値問題 / 空間高次元 / 2次モーメント / 高次元 / 移流拡散方程式系 / 時間大域解 / 走化性 / 閾値 / 移流拡散方程式 / 爆発解 / 粘菌 / 空間2次元
Outline of Final Research Achievements

We have considered a drift-diffusion system which is not one component.At first, we have studied a drift-diffusion system on bounded domain in two space dimension. Then we have performed the blowup analysis such as the formation of collapses and collapsemass separations. And we have discussed the blow-up conditions for multicomponent drift-diffusion model in two space dimension and higher dimensions, respectively. Moreover We have shown that the local solvability of the solution in the weighted L2 spaces and the extention of the functional space for the solution in two space dimension.In higher dimension case, we have applied the Shannon entropy inequality to lead the blow up condition for a drift-diffusion system.

Report

(5 results)
  • 2015 Annual Research Report   Final Research Report ( PDF )
  • 2014 Research-status Report
  • 2013 Research-status Report
  • 2012 Research-status Report
  • Research Products

    (22 results)

All 2016 2015 2014 2013 Other

All Journal Article (5 results) (of which Peer Reviewed: 5 results,  Acknowledgement Compliant: 2 results) Presentation (17 results) (of which Int'l Joint Research: 2 results,  Invited: 14 results)

  • [Journal Article] Finite time blow up for a solution to system Of the drift-diffusion equations in higher dimensions,2016

    • Author(s)
      Masaki Kurokiba, Takayoshi Ogawa
    • Journal Title

      Mathematische Zeitschrift

      Volume: 0 Issue: 1-2 Pages: 0-0

    • DOI

      10.1007/s00209-016-1654-5

    • Related Report
      2015 Annual Research Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] Two Dimestional drift-diffusion system in a critical weighted space2015

    • Author(s)
      Masaki Kurokiba, Takayoshi Ogawa
    • Journal Title

      Differential and Integral Equations

      Volume: 28 Pages: 753-776

    • Related Report
      2014 Research-status Report
    • Peer Reviewed / Acknowledgement Compliant
  • [Journal Article] On a perturbed system of chemotaxis, II2014

    • Author(s)
      Masaki Kurokiba, Takashi Suzuki, Ryo Takahashi
    • Journal Title

      International Journal of Pure and Applied Mathematics

      Volume: 92 Issue: 3 Pages: 305-334

    • DOI

      10.12732/ijpam.v92i3.1

    • Related Report
      2014 Research-status Report
    • Peer Reviewed
  • [Journal Article] Existence and blowing up for a system of the drift-diffusion equation in R22014

    • Author(s)
      Masaki Kurokiba
    • Journal Title

      Differential and Integral Equations

      Volume: 27 Pages: 425-446

    • Related Report
      2013 Research-status Report
    • Peer Reviewed
  • [Journal Article] Blowup Threshold and Cllapse Mass Separation for a Drift-Diffusion System in Space-Dimension Two2013

    • Author(s)
      Elio Espejo, Masaki Kurokiba, Takashi Suzuki
    • Journal Title

      Communications on Pure and Applied Analysis

      Volume: Vol.12

    • Related Report
      2012 Research-status Report
    • Peer Reviewed
  • [Presentation] Blowing up for a solution to system of the drift-diffusion equations in higher space dimensions2016

    • Author(s)
      黒木場正城
    • Organizer
      Second Workshop on Nonlinear Dispersive Equations
    • Place of Presentation
      IMECC-UNICAMP, Campinas, Brazil,
    • Year and Date
      2016-10-06
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research
  • [Presentation] 高次元移流拡散方程式系の解の有限時間爆発について2016

    • Author(s)
      黒木場正城
    • Organizer
      2016年日本数学会年会函数方程式論分科会特別講演
    • Place of Presentation
      筑波大学
    • Year and Date
      2016-03-16
    • Related Report
      2015 Annual Research Report
    • Invited
  • [Presentation] Blowing up for a solution to system of the drift-diffusion equations in three dimension2015

    • Author(s)
      黒木場正城
    • Organizer
      ISAAC 2015
    • Place of Presentation
      University of Macau Macao, China
    • Year and Date
      2015-08-03
    • Related Report
      2015 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Blowing up for a system of the driift-diffusion equation in R32015

    • Author(s)
      黒木場正城
    • Organizer
      研究集会 Critical Exponents and Nonlinear Evolution Equation 2015
    • Place of Presentation
      東京理科大学神楽坂キャンパス(東京都新宿区)
    • Year and Date
      2015-02-21
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] Blowing up for a system of the drift-diffusion equation in R32014

    • Author(s)
      黒木場正城
    • Organizer
      北海道大学PDEセミナー
    • Place of Presentation
      北海道大学大学院理学研究科(北海道札幌市)
    • Year and Date
      2014-12-26
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] Finite time blow up for a solution to system of the drift-diffusion equations in three dimensions2014

    • Author(s)
      黒木場正城
    • Organizer
      中華民国數学会
    • Place of Presentation
      国立成功大学(中華民国台北)
    • Year and Date
      2014-12-07
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] Two dimensional drift-diffusion system in a critical weighted space2014

    • Author(s)
      黒木場正城
    • Organizer
      2014年日本秋季数学会総合分科会
    • Place of Presentation
      広島大学(広島県東広島市)
    • Year and Date
      2014-09-28
    • Related Report
      2014 Research-status Report
  • [Presentation] 空間3次元 drift-diffusion system の初期値問題に対する有限時間爆発解について2014

    • Author(s)
      黒木場正城
    • Organizer
      愛媛大学解析セミナー
    • Place of Presentation
      愛媛大学理学部(愛媛県松山市)
    • Year and Date
      2014-05-24
    • Related Report
      2014 Research-status Report
    • Invited
  • [Presentation] Existence and blowing up for a system of the drift-diffusion equation in R22013

    • Author(s)
      黒木場正城
    • Organizer
      研究集会「第9回非線型の諸問題」
    • Place of Presentation
      高知大学朝倉キャンパス( 高知県高知市 )
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] Existence and blowing up for a system of the drift-diffusion equation in R2

    • Author(s)
      黒木場正城
    • Organizer
      第562回応用解析研究会
    • Place of Presentation
      早稲田大学理工学部( 東京都新宿区 )
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] Existence and blowing up for a system of the drift-diffusion equation in R2

    • Author(s)
      黒木場正城
    • Organizer
      Analysis/PDE seminar
    • Place of Presentation
      Department of Mathematics, University of Calfornia, Santa Barbara, United States of America
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] Existence and blowing up for a system of the drift-diffusion equation in R2

    • Author(s)
      黒木場正城
    • Organizer
      RIMS研究集会「抽象的発展方程式の新たなる役割」
    • Place of Presentation
      京都大学数理解析研究所( 京都府京都市左京区 )
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] Existence and blowing up for a system of the drift-diffusion equation in R2

    • Author(s)
      黒木場正城
    • Organizer
      北海道大学PDEセミナー
    • Place of Presentation
      北海道大学大学院理学研究科( 北海道札幌市 )
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] Existence and blowing up for a system of the drift-diffusion equation in R2

    • Author(s)
      黒木場正城
    • Organizer
      第11回浜松偏微分方程式研究集会
    • Place of Presentation
      静岡大学工学部( 静岡県浜松市 )
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] Existence and blowing up for a system of the drift-diffusion equation in R2

    • Author(s)
      黒木場正城
    • Organizer
      名古屋微分方程式セミナー
    • Place of Presentation
      名古屋大学大学院多元数理科学研究科( 愛知県名古屋市 )
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] Existence and blowing up for a system of the drift-diffusion equation in R2

    • Author(s)
      黒木場正城
    • Organizer
      研究集会「Workshop on analysis in Kagurazaka」
    • Place of Presentation
      東京理科大学理学部( 東京都新宿区 )
    • Related Report
      2013 Research-status Report
    • Invited
  • [Presentation] Existence and blowing up for a system of the drift-diffusion equation in R2

    • Author(s)
      黒木場正城
    • Organizer
      第15回北東数学解析研究会
    • Place of Presentation
      北海道大学大学院理学研究科( 北海道札幌市 )
    • Related Report
      2013 Research-status Report
    • Invited

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Published: 2013-05-31   Modified: 2019-07-29  

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