| Abstract: |
| We investigate the existence of the non-radial steady states of the Keller-Segel model in a bounded convex planar domain that is symmetric with respect to two orthogonal directions via global bifurcation. It is shown that non-radial steady states exist if the chemotactic coefficient exceeds a critical threshold. To model the cell aggregation, one of the most important phenomena in chemotaxis, we also show that boundary spiky solutions exist if the chemotactic coefficient tends to infinity. Our results provide a new insight on the mechanism of the pattern formation and cell aggregation in a bounded convex planar domain with two orthogonal directions. |
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