| Abstract: |
| This talk describes the properties of classical solutions to a particular class of chemotaxis systems consisting of three partial differential equations that are either fully parabolic or comprises one parabolic equation along with two others that are elliptic. The primary goal of our investigation is to explore the global existence and potential blow-up of such solutions within bounded domains of $\mathbb{R}^n$, $n \geq 3$, subject to homogeneous Neumann boundary conditions. We establish the global-in-time existence and uniform boundedness of the solutions under smallness conditions imposed on the initial data. Furthermore, we present estimates for the blow-up time of unbounded solutions in three-dimensional space, which are corroborated by numerical simulations. |
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