On new approch for wellposedness for degenerate and singular Keller-Segel systems

2014 Fiscal Year Final Research Report

• Project/Area Number: 24540186
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Basic analysis
• Research Institution: Kyushu University
• Principal Investigator: SUGIYAMA Yoshie 九州大学, 大学院・数理学研究院, 教授 (60308210)
• Project Period (FY): 2012-04-01 – 2015-03-31
• Keywords: 退化放物型方程式 / Keller-Segel系 / 初期値問題の局所適切性 / 解の一意性 / 解の有限時間爆発 / Navier-Stokes方程式

Outline of Final Research Achievements

The Keller-Segel system contains several parameters which cause numerous structures such as linear, degenerate and singular type of PDE. In particular, the degenerate type contains the unknown function as the coefficients breaking down uniform ellipticity, which makes the problem more difficult in comparison with the other types.
The Keller-Segel system itself is characterized as the parabolic-parabolic and parabolic-elliptic both of provide us an important research theme. Indeed, we need to handle these types in accordance with the characteristic features of equations. In this talk, we shall bring a focus onto the parabolic-parabolic and parabolic-elliptic Keller-Segel systems of the singular and degenerate types and show uniqueness of weak solutions in the class of Hoelder continuous functions.

Free Research Field

非線形偏微分方程式論