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

2016 Fiscal Year Final Research Report

• 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
• Keywords: 抽象偏微分方程式 / 個体数モデル

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.

Free Research Field

解析学