| Abstract: |
| Bacillus subtilis swim toward oxygen-rich air-water interfaces in water droplets and form large clusters near the boundary. To describe such pattern formation, chemotaxis systems with signal consumption have been proposed, which in numerical studies have exhibited various patterns similar to those observed in actual experiments. In this talk, I will present related analytical results on chemotaxis-consumption systems, particularly those with Dirichlet boundary conditions for the signal. One of our findings shows that bacteria populations under certain initial conditions tend to aggregate near the boundary, where signals have been prescribed. On the other hand, for the system of chemorepulsive counterpart, it is shown that a finite time blowup can be observed whenever the diffusion effect on bacteria populations is slightly weakened. Some results on the existence of bounded solutions will also be discussed. |
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