We study this zero-flux attraction–repulsion chemotaxis model, with linear and superlinear production $g$ for the chemorepellent and sublinear rate $f$ for the chemoattractant: ($♢$)$\left\{\begin{array}{cc}{u}_t=\Delta u-\chi \nabla \cdot (u\nabla v)+\xi \nabla \cdot (u\nabla w)\hfill & \text{in }\Omega \times (0,T_{max}),\hfill \\ v_t=\Delta v-f\left(u\right)v\hfill & \text{in }\Omega \times (0,T_{max}),\hfill \\ 0=\Delta w-\delta w+g\left(u\right)\hfill & \text{in }\Omega \times (0,T_{max}).\hfill \end{array}\right.$In this problem, $\Omega$ is a bounded and smooth domain of ${\mathbb{R}}^n$, for $n\ge 1$, $\chi ,\xi ,\delta >0$, $f\left(u\right)$ and $g\left(u\right)$ reasonably regular functions generalizing the prototypes $f\left(u\right)=K{u}^{\alpha }$ and $g\left(u\right)=\gamma u^l$, with $K,\gamma >0$ and proper $\alpha ,l>0$. Once it is indicated that any sufficiently smooth $u(x,0)=u_0\left(x\right)\ge 0$ and $v(x,0)=v_0\left(x\right)\ge 0$ produce a unique classical and nonnegative solution $(u,v,w)$ to (1), which is defined in $\Omega \times (0,T_{max})$, we establish that for any such $(u_0,v_0)$, the life span $T_{max}=\infty$ and $u,v$ and $w$ are uniformly bounded in $\Omega \times (0,\infty )$, (i) for $l=1$, $n\in \{1,2\}$, $\alpha \in (0,\frac{1}{2}+\frac{1}{n})\cap (0,1)$ and any $\xi >0$, (ii) for $l=1$, $n\ge 3$, $\alpha \in (0,\frac{1}{2}+\frac{1}{n})$ and $\xi$ larger than a quantity depending on $\chi \Vert v_0{\Vert }_{L^{\infty }\left(\Omega \right)}$, (iii) for $l>1$, $\alpha \in (0,\frac{1}{2}+\frac{1}{n})\cap (0,1)$, any $\xi >0$, and in any dimensional settings. Finally, an illustrative analysis about the effect by logistic and repulsive actions on chemotactic phenomena is proposed by comparing the results herein derived for the linear production case with those in Lankeit and Wang (2017).

我们研究了这种具有线性和超线性产生的零通量吸引-排斥趋化模型 $G$ 对于化学驱避剂和亚线性速率 $F$对于趋化：（$♢$)$\left\{\begin{array}{cc}{你}_{吨}=\Delta 你-\chi \nabla \cdot (你\nabla v)+\xi \nabla \cdot (你\nabla 瓦)\hfill & \text{在 }\Omega \times (0,{吨}_{米\mathrm{一种}X}),\hfill \\ v_{吨}=\Delta v-F\left(你\right)v\hfill & \text{在 }\Omega \times (0,{吨}_{米\mathrm{一种}X}),\hfill \\ 0=\Delta 瓦-\delta 瓦+G\left(你\right)\hfill & \text{在 }\Omega \times (0,{吨}_{米\mathrm{一种}X}).\hfill \end{array}\right.$在这个问题中， $\Omega$ 是一个有界且光滑的域 ${\mathbb{电阻}}^n$， 为了 $n\ge 1$, $\chi ,\xi ,\delta >0$, $F\left(你\right)$ 和 $G\left(你\right)$ 泛化原型的合理正则函数 $F\left(你\right)=钾{你}^{\alpha }$ 和 $G\left(你\right)=\gamma {你}^{升}$， 和 $钾,\gamma >0$ 和适当的 $\alpha ,升>0$. 一旦表明任何足够光滑$你(X,0)={你}_0\left(X\right)\ge 0$ 和 $v(X,0)=v_0\left(X\right)\ge 0$ 产生一个独特的经典和非负解 $(你,v,瓦)$ 到（1），其定义在 $\Omega \times (0,{吨}_{米\mathrm{一种}X})$，我们确定对于任何这样的 $({你}_0,v_0)$，寿命 ${吨}_{米\mathrm{一种}X}=\infty$ 和 $你,v$ 和 $瓦$ 均匀地有界于 $\Omega \times (0,\infty )$, (i) 对于 $升=1$, $n\in \{1,2\}$, $\alpha \in (0,\frac{1}{2}+\frac{1}{n})\cap (0,1)$ 和任何 $\xi >0$, (ii) 对于 $升=1$, $n\ge 3$, $\alpha \in (0,\frac{1}{2}+\frac{1}{n})$ 和 $\xi$ 大于数量取决于 $\chi \Vert v_0{\Vert }_{{升}^{\infty }\left(\Omega \right)}$, (iii) 对于 $升>1$, $\alpha \in (0,\frac{1}{2}+\frac{1}{n})\cap (0,1)$， 任何 $\xi >0$，以及在任何维度设置中。最后，通过将本文针对线性生产案例得出的结果与 Lankeit 和 Wang (2017) 的结果进行比较，提出了关于逻辑和排斥作用对趋化现象的影响的说明性分析。