2017 Fiscal Year Final Research Report
The dynamics of a system of a single reaction-diffusion equation coupled with an ordinary differential equation
| Project/Area Number |
26400156
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Multi-year Fund |
|---|
| Section | 一般 |
|---|
| Research Field |
Mathematical analysis
|
|---|
| Research Institution | Ibaraki University |
|---|
Principal Investigator |
|
|---|
| Project Period (FY) |
2014-02-01 – 2018-03-31
|
| Keywords | 反応拡散系 / パターン形成 / 解の爆発 |
|---|
| Outline of Final Research Achievements |
The dynamics of a system of a single reaction-diffusion equation coupled with an ordinary differential equation was studied. Such systems arise, for example, from modeling of interactions between processes in cells and diffusing signaling factors. I particularly considered the blowup phenomena to understand a relationship between the dynamics and a diffusion-driven instability, which is a mechanism to obtain spatially heterogeneous states in pattern formation phenomena.
It was shown that the system has blowup solutions and, depending on nonlineality, they can blow up either in finite or infinite time. Concerning the blowup in finite time, sufficient conditions for initial data are obtained, and we could see the shape of solutions at blowup time. Moreover, it was shown that some systems have unbounded week stationary solutions, which can be key to understand the mechanism of blowup infinite time.
|
| Free Research Field |
非線形解析学
|
