On blowup points and asymptotic behavior of blowup solutions to a simplified chemotaxis system
| Project/Area Number |
15540176
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Single-year Grants |
|---|
| Section | 一般 |
|---|
| Research Field |
Basic analysis
|
|---|
| Research Institution | University of Miyazaki |
|---|
Principal Investigator |
SENBA Takasi University of Miyazaki, Fac. of Engineering, Professor, 工学部, 教授 (30196985)
|
|---|
| Co-Investigator(Kenkyū-buntansha) |
TSUJIKAWA Tohru University of Miyazaki, Fac. of Engineering, Professor, 工学部, 教授 (10258288)
KABEYA Yoshitsugu Osaka Prefecture University, School of Engineering, Assistant Professor, 大学院・工学研究科, 助教授 (70252757)
|
|---|
| Project Period (FY) |
2003 – 2005
|
| Project Status |
Completed (Fiscal Year 2005)
|
| Budget Amount *help |
¥2,800,000 (Direct Cost: ¥2,800,000)
Fiscal Year 2005: ¥800,000 (Direct Cost: ¥800,000)
Fiscal Year 2004: ¥900,000 (Direct Cost: ¥900,000)
Fiscal Year 2003: ¥1,100,000 (Direct Cost: ¥1,100,000)
|
|---|
| Keywords | Chemotaxis system / Keller-Segel system / Blowup solution / Type I blowup / Type II blowup / 偏微分方程式 / 生物モデル / Keller-Segel系 / 解の爆発 / 走化性 |
|---|
| Research Abstract |
The aim of This research is the investigation of behavior of blowup solutions of a simplified chemotaxis system in two spatial dimensions.
Before this research, the following are shown.
・At blowup points and blowup time, the solutions have singularities.
・Each singularity is equal to a positive constant times the delta function.
・The positive constant is equal to a threshold number or more.
Then, the aim of this research is the investigation of quantity of the positive constant.
In order to determine the quantity, we use a resealing. By the resealing, the blowup time is translated to the infinity. Then, we show the following.
If the rescaling solutions grow up, the solutions satisfy the following
・The rescaling solutions have singularities at the infinite time.
・Each singularity is equal to the threshold number times the delta function.
As stated above, we approach the answer of our problem.
|
Report
(4 results)
Research Products
(26 results)
