Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5774275 | Journal of Differential Equations | 2017 | 46 Pages |
Abstract
We prove the existence of assemblies of interior and boundary spikes as stationary solutions of the two-dimensional Gierer-Meinhardt system. Moreover, we also discover that the locations of the spikes are determined by the curvature of the domain boundary together with the Green's function of the domain. A reflection operator of âÎ is introduced to study the behaviour of the regular part of Green's function around the boundary. This reflection generalizes the well-known notions of mirror image and circle inversion for domains with sufficiently smooth boundary.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Yeyao Hu,