| Abstrakt: |
In this paper, we consider the existence and the linear stability of spiky stationary solutions for the Gierer-Meinhardt model with heterogeneity on the Y-shaped compact metric graph. The existence is shown by the Liapunov-Schmidt reduction method, and the stability is shown by investigating the associated linearized eigenvalue problem. In particular, it is revealed that the location, amplitude, and stability of spikes are decided by the interaction of the heterogeneity functions with the geometry of the graph, represented by the associated Green's function. Moreover, by applying our abstract theorem to several concrete examples, we study the detailed effects of the geometry of the graph and the heterogeneity function on spiky solutions. [ABSTRACT FROM AUTHOR] |
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