• Search Research Projects
  • Search Researchers
  • How to Use
  1. Back to previous page

On the structure analysis of measure value solutions and singular sets for non-linear drift diffusion systems

Research Project

Project/Area Number 19K03561
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Review Section Basic Section 12020:Mathematical analysis-related
Research InstitutionOsaka University

Principal Investigator

Yoshie Sugiyama  大阪大学, 情報科学研究科, 教授 (60308210)

Project Period (FY) 2019-04-01 – 2022-03-31
Project Status Completed (Fiscal Year 2021)
Budget Amount *help
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2021: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2020: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2019: ¥2,470,000 (Direct Cost: ¥1,900,000、Indirect Cost: ¥570,000)
KeywordsKeller-Segel系 / 測度値解 / 時間大域解 / 初期著問題の適切性 / 特異性解析 / 局所適切性 / 特異性 / Navier-Stokes方程式 / 閾値 / 移流拡散
Outline of Research at the Start

本申請研究ではKeller-Segel系の解構造を大きい初期値と小さい初期値のいずれの場合にも議論し,統一的に描出することを研究目的とする.
① 近似解とその極限測度としての測度値解の存在:初期値のサイズに依存せずに時間
大域的に測度値解の構成を試みる.
② 測度値解の表現:測度値解は全ての時刻で「デルタ関数の有限和と正則部分」との総和で表現を有するかどうかを考察する.
③ 爆発点の軌跡を考察する.④ 凝集のサイズを考察する.⑤ 爆発点の位置を考察する.

Outline of Final Research Achievements

We consider not only linear diffusion but also nonlinear diffusion Keller-Sgel systems, and prove that the metric solution is described by the sum of the finite sum of the δ-functions and the regular part at every time step. Furthermore, we succeeded in proving the following:
(1) Whether or not the solution is constructed beyond the explosion time. Whether there exists an appropriate solution space for this purpose. (2) Whether the trajectory of the explosion point (the center of the aggregation of δ-functions) is regular as a time function. (3) Whether the size of the cohesion of the explosion point is regular and monotonic as a function of time.

Academic Significance and Societal Importance of the Research Achievements

本研究では,爆発点の集合及び凝集サイズの時間発展を解析することで,解の有する特異構造を詳らかしている.初期値のサイズに依存しないKeller-Segel系の解構造について,統一理論を構築したことで,特異性を有する方程式系の解析に新たな数学的枠組みを構築することが出来た.

Report

(3 results)
  • 2021 Final Research Report ( PDF )
  • 2020 Research-status Report
  • 2019 Research-status Report
  • Research Products

    (1 results)

All 2019

All Journal Article (1 results) (of which Peer Reviewed: 1 results)

  • [Journal Article] Time global existence and finite time blow-up criterion for solutions to the Keller-Segel system coupled with the Navier-Stokes fluid2019

    • Author(s)
      Kozono, Hideo; Miura, Masanari; Sugiyama, Yoshie .
    • Journal Title

      J. Differential Equations

      Volume: 267

    • Related Report
      2019 Research-status Report
    • Peer Reviewed

URL: 

Published: 2019-04-18   Modified: 2023-12-25  

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi