| Abstract: |
| In this work, to address the asymptotic stability of chemotaxis systems incorporating various mechanisms, we employ the De Giorgi iteration method to quantitatively analyze the upper bound of solutions.
The refined upper bound estimate obtained in the present paper illustrates how various factors influence the upper bound, which can then be used to determine the large-time behaviours of solutions. To show the wide applicability of our findings, we investigate the asymptotic stability of a chemotaxis model with nonlinear signal production and a chemotaxis-Navier-Stokes model with a logistic source.
Additionally, within the context of $p$-Laplacian diffusion, we establish H\"{o}lder continuity for a chemotaxis-haptotaxis model and a chemotaxis-Stokes model. |
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