| Abstract: |
| In this talk, we will discuss results concerning the solvability of a chemotaxis model, which describes the movement of organisms in response to chemical substances. Focusing on the repulsive chemotaxis-consumption system, we examine the criteria under which solutions remain bounded over time and the conditions leading to blow-up in higher dimensions. Specifically, we show that the system admits globally bounded solutions when the diffusion of the organisms is enhanced, or when the diffusion is weakened but the boundary data for the signal substance is sufficiently small. On the other hand, we prove that if the diffusion is further weakened and the boundary data for the signal is sufficiently large, the system exhibits blow-up behavior. |
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