## 講演会

### 2012年11月22日(木)

13:30-14:15   数理科学研究科棟(駒場) 002号室

Danielle Hilhorst 氏 (CNRS / Univ. Paris-Sud)
A multiple scale pattern formation cascade in reaction-diffusion systems of activator-inhibitor type (ENGLISH)
[ 講演概要 ]
A family of singular limits of reaction-diffusion systems of activator-inhibitor type in which stable stationary sharp-interface patterns may form is investigated. For concreteness, the analysis is performed for the FitzHugh-Nagumo model on a suitably rescaled bounded domain in $\\R^N$, with $N \\geq 2$. It is proved that when the system is sufficiently close to the limit the dynamics starting from the appropriate smooth initial data breaks down into five distinct stages on well-separated time scales, each of which can be approximated by a suitable reduced problem. The analysis allows to follow fully the progressive refinement of spatiotemporal patterns forming in the systems under consideration and provides a framework for understanding the pattern formation scenarios in a large class of physical, chemical, and biological systems modeled by the class of reaction-diffusion equations, which we consider. This is joint work with Marie Henry and Cyrill Muratov.
[ 参考URL ]
https://www.ms.u-tokyo.ac.jp/gcoe/index_007.html