2018 Fiscal Year Final Research Report
Theory for the mathematical modeling of complicated systems
| Project/Area Number |
26310212
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (B)
|
| Allocation Type | Partial Multi-year Fund |
|---|
| Section | 特設分野 |
|---|
| Research Field |
Mathematical Sciences in Search of New Cooperation
|
|---|
| Research Institution | Hokkaido University |
|---|
Principal Investigator |
|
|---|
| Project Period (FY) |
2014-07-18 – 2019-03-31
|
| Keywords | スポット解 / 相互作用 / 中心多様体 |
|---|
| Outline of Final Research Achievements |
The motion of spot-like localized solutions was successfully derived by combining weak interaction and bifurcation approaches for multi-variable reaction-diffusion systems. The results were applied to the analysis of the interaction between two camphor tips with elliptic shapes and the theoretically reduced motion was checked in real experiments. The results were also applied to the motion of spot solution on a curved surface and the motion depending on the gradient of Gaussian curvature of the surface was derived.
|
| Free Research Field |
非線形解析
|
| Academic Significance and Societal Importance of the Research Achievements |
現象を数理モデルによりある程度忠実に記述する際, 多数の未知変数が必要となったり, 非線形項などをきちんと決めることができないといった状況が生じる．そのような場合でも, 分岐構造や相互作用といった, 実験により容易に検証可能な条件のみで理論的に帰結できる普遍的な解の性質を導いたことは, モデルの検証として役立つと同時に, 解の本質的構造の理解につながると期待される．
|
