On the structure of blowup solutions to chemotaxis systems

2014 Fiscal Year Final Research Report

• Project/Area Number: 22540200
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Single-year Grants
• Section: 一般
• Research Field: Basic analysis
• Research Institution: Kyushu Institute of Technology
• Principal Investigator: SENBA Takasi 九州工業大学, 工学(系)研究科(研究院), 教授 (30196985)
• Project Period (FY): 2010-04-01 – 2015-03-31
• Keywords: 走化性方程式 / 後方自己相似解 / 定常解 / 安定性

Outline of Final Research Achievements

From 2010 to 2014, we consider properties of solutions to chemotaxis system. In particular, we consider stability of backward self-similar solutions and stationary solutions.
First, we consider properties of backward self-similar solutions. The backward self-similar solutions are one of typical blowup solutions. We showed some stability of the solutions. The solutions are not so many. However, it became clear by our research that many solutions have similar properties to the backward self-similar solutions.
Next, we consider stability of stationary solutions to chemotaxis system. It was well known that radial stationary solutions are stable in two dimensional case. We showed that radial stationary solutions are stable also in high dimensional cases. Moreover, by using stability, we construct oscillatory solutions and infinite time blowup solutions.

Free Research Field

関数方程式論