| Abstract: |
| In this talk, we consider the Schnakenberg model on compact metric graphs with heterogeneity in front of the nonlinear term. The one-dimensional interval case was studied by e.g. Ishii and Kurata (2019). We first establish the abstract theorem on the existence of multi-peak stationary solutions on general compact metric graphs under several assumptions for the associated Green`s function. In particular, we reveal the effect of the geometry of the compact metric graph and the heterogeneity on the existence. Next, we apply our abstract theorem to the $Y$-shaped metric graph in non-heterogeneity case. In particular, we describe the effect of the geometry of this metric graph on the location of concentration points, which is a new phenomenon compared with one-dimensional interval case. This is a joint work with Prof. Kazuhiro Kurata. |
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