Global existence and boundedness of classical solutions of the chemotaxis--consumption system \begin{align*} n_t &= \Delta n - \nabla \cdot (n \nabla c), \\ 0 &= \Delta c - nc, \end{align*} under no-flux boundary conditions for $n$ and Robin-type boundary conditions \[ \partial_{\nu} c = (\gamma-c) g \] for $c$ (with $\gamma>0$ and $C^{1+\beta}(\partial\Omega) \ni g > 0$ for some $\beta\in(0,1)$) are established in bounded domains $\Omega\subset\mathbb{R}^{N}$, $N\ge 1$. Under a smallness condition on $\gamma$, moreover, we show convergence to the stationary solution.

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抛物线-椭圆趋化-消耗模型中的长期行为

趋化性经典解的全局存在性和有界性--消耗系统 \begin{align*} n_t &= \Delta n - \nabla \cdot (n \nabla c), \\ 0 &= \Delta c - nc, \ end{align*} 在无通量边界条件下 $n$ 和 Robin 型边界条件 \[ \partial_{\nu} c = (\gamma-c) g \] 对于 $c$（与 $\gamma> 0$ 和 $C^{1+\beta}(\partial\Omega) \ni g > 0$ for some $\beta\in(0,1)$) 在有界域 $\Omega\subset\mathbb 中建立{R}^{N}$，$N\ge 1$。此外，在 $\gamma$ 的小条件下，我们展示了对平稳解的收敛性。