From abstract evolution equations to abstract partial differential equations - for applications to population dynamics models

• Project/Area Number: 25400140
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Basic analysis
• Research Institution: Kanazawa University (2014-2016); Shimane University (2013)
• Principal Investigator: Kato Nobuyuki 金沢大学, 電子情報学系, 教授 (40177423)
• Co-Investigator(Renkei-kenkyūsha): SAITO Yasuhisa 島根大学, 総合理工学部, 准教授 (30402241) ; SUGIE Jitsuro 島根大学, 総合理工学部, 教授 (40196720) ; SETO Michio 防衛大学校, 総合教育学群, 准教授 (30398953) ; KUROIWA Daishi 島根大学, 総合理工学部, 教授 (40284020)
• Project Period (FY): 2013-04-01 – 2017-03-31
• Project Status: Completed (Fiscal Year 2016)
• Budget Amount: ¥4,810,000 (Direct Cost: ¥3,700,000、Indirect Cost: ¥1,110,000); Fiscal Year 2016: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000); 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)
• Keywords: 抽象偏微分方程式 / 個体数モデル / 個体数変動モデル / 最適制御 / 個体数変動 / 発展方程式 / サイズ / 拡散

Outline of Final Research Achievements

We have considered some population models living in a habitat. Here, the mortality, the reproduction, and the inflow are supposed to depend on the individual’s size, time and position. In addition, each individual is supposed to spread in the habitat. In this research, as a new framework to analyze such models, we have intended to introduce and develop a theory of abstract partial differential equations. As a basic theory, we have established the existence and uniqueness of solutions, continuous dependence on initial data and positivity of solutions. Also, we have investigated comparison theorem, the dual problem and uniqueness of weak solutions.

Research Products

• [Int'l Joint Research] プレーリー・ビュー A&M 大学/ヒューストン・バプティスト大学(米国)
• [Int'l Joint Research] スターリング大学(英国)
• [Journal Article] Optimal control of investments in old and new capital under improving technology (2017)
  • Author(s): N. Hritonenko, N. Kato, Yu. Yatsenko
  • Journal Title: J. Optim. Theory Appl. Volume: 172 Issue: 1 Pages: 247-266
  • DOI: 10.1007/s10957-016-1022-y
  • Peer Reviewed / Int'l Joint Research
• [Journal Article] Abstract linear partial differential equations related to size-structured population models with diffusion (2016)
  • Author(s): Nobuyuki Kato
  • Journal Title: J. Math. Anal. Appl. Volume: 436 Issue: 2 Pages: 890-910
  • DOI: 10.1016/j.jmaa.2015.11.077
  • NAID: 120005708448
  • Peer Reviewed / Acknowledgement Compliant
• [Journal Article] Linear size-structured population models with spacial diffusion and optimal harvesting problems (2014)
  • Author(s): Nobuyuki Kato
  • Journal Title: Math. Model. Nat. Phenom. Volume: 9 Issue: 4 Pages: 122-130
  • DOI: 10.1051/mmnp/20149408
  • NAID: 120005466948
  • Peer Reviewed / Acknowledgement Compliant
• [Presentation] Partial differential equations in Banach lattices related to size-structured population models (2015)
  • Author(s): Nobuyuki Kato
  • Organizer: Equadiff 2015
  • Place of Presentation: Université Claude Bernard Lyon 1
  • Year and Date: 2015-07-06
  • Int'l Joint Research
• [Presentation] Size-structured population models with diffusion (2014)
  • Author(s): Nobuyuki Kato
  • Organizer: AIMS2014
  • Place of Presentation: Universidad Autonoma de Madrid, Madrid, Spain
  • Year and Date: 2014-07-07 – 2014-07-11
• [Presentation] Abstract size-structured population dynamics in Banach spaces (2013)
  • Author(s): Nobuyuki Kato
  • Organizer: Equadiff2013
  • Place of Presentation: Prague, Czech Republic