Project/Area Number  09640204 
Research Category 
GrantinAid for Scientific Research (C)

Section  一般 
Research Field 
解析学

Research Institution  KYUSHU INSTITUTE OF TECHNOLOGY 
Principal Investigator 
NAGAI Toshitaka KYUSHU INSTITUTE OF TECHNOLOGY,Faculty of Engineering, Professor, 工学部, 教授 (40112172)

CoInvestigator(Kenkyūbuntansha) 
SENBA Takashi Miyazaki University, Faculty of Technology, Associate Professor, 工学部, 助教授 (30196985)

Project Fiscal Year 
1997 – 1998

Project Status 
Completed(Fiscal Year 1998)

Budget Amount *help 
¥3,000,000 (Direct Cost : ¥3,000,000)
Fiscal Year 1998 : ¥1,300,000 (Direct Cost : ¥1,300,000)
Fiscal Year 1997 : ¥1,700,000 (Direct Cost : ¥1,700,000)

Keywords  Advectiondiffusion system / Global existence of solutions / Blowup of solutions / Singularity of solutions / 移流拡散方程式系 / 解の大域的存在 / 解の爆発 / 解の特異性 / 移流拡散方程式 / 解の時間大域的存在 / 解の挙動 / 関数の対称化 
Research Abstract 
The purpose of this research is to study the qualitative properties of an advectiondiffusion equationcalled a chemotaxis system. This system is a mathematical model describing chemotactic aggregation of cellular slime molds which move towards relatively higher concentration of a chemical. We studied the global existence of solutions and finitetime blowup of solutions to the chemotaxis system and obtained the following results. 1. Two types of sensitivity functions are considered to study the structure of the global existence and blowup of solutions, and it was shown that the structure of radial solutions entirely depends on the sensitivity functions. 2. It was shown that the finitetime blowup of solutions to an parabolicelliptic system, which is a simplified version of the chemotaxis system, necessarily leads to chemotactic collapse (the blowup with 6function singularities) at an isolated blowup point in twodimensional domains. 3. The application of syrnmetrization techniques to the parabolicelliptic system mentioned above is effective to obtain Drestimates of solutions in terms of L^p norm of initial functions.
