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Dynamics of a boundary spike for the shadow Gierer-Meinhardt system
| Content Provider | Semantic Scholar |
|---|---|
| Author | Ei, Shin-Ichiro Ikeda, Kota Miyamoto, Yasuhito |
| Copyright Year | 2011 |
| Abstract | The Gierer-Meinhardt system is a mathematical model describing the process of hydra regeneration. The authors of [3] showed that if an initial value is close to a spiky pattern and its peak is far away from the boundary, the solution of the shadow Gierer-Meinhardt system, called a interior spike solution, moves towards a point on boundary which is the closest to the peak. However it has not been studied how a solution close to a spiky pattern with the peak on the boundary, called a boundary spike solution moves along the boundary. In this paper, we consider the shadow Gierer-Meinhardt system and dynamics of a boundary spike solution. Our results state that a boundary spike moves towards a critical point of the curvature of the boundary and approaches a stable stationary solution. |
| Starting Page | 115 |
| Ending Page | 145 |
| Page Count | 31 |
| File Format | PDF HTM / HTML |
| DOI | 10.3934/cpaa.2012.11.115 |
| Volume Number | 11 |
| Alternate Webpage(s) | https://catalog.lib.kyushu-u.ac.jp/opac_download_md/27285/83_ei.pdf |
| Alternate Webpage(s) | https://doi.org/10.3934/cpaa.2012.11.115 |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
