| Abstract: |
| In this presentation, we explore the parabolic-elliptic chemotaxis-consumption system of repulsion type in higher dimensions under no-flux/Dirichlet boundary conditions. We discuss the criteria for solutions to remain bounded over time and the conditions under which blow-up occurs. Specifically, we show that the system admits globally bounded solutions when the diffusion of the organisms is enhanced, or when it is weakened but the boundary data for the signal substance is sufficiently small. Furthermore, we demonstrate that when the diffusion is further weakened and the boundary data for the signal is appropriately large, the system possesses blow-up solutions. |
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