We consider a chemo-repulsion model with quadratic production in a bounded domain. Firstly, we obtain global in time weak solutions, and give a regularity criterion (which is satisfied for $1D$ and $2D$ domains) to deduce uniqueness and global regularity. After, we study two cell-conservative and unconditionally energy-stable first-order time schemes: a (nonlinear and positive) Backward Euler scheme and a linearized coupled version, proving solvability, convergence towards weak solutions and error estimates. In particular, the linear scheme does not preserve positivity and the uniqueness of the nonlinear scheme is proved assuming small time step with respect to a strong norm of the discrete solution. This hypothesis is reduced to small time step in $nD$ domains ($n\le 2$) where global in time strong estimates are proved. Finally, we show the behavior of the schemes through some numerical simulations.

我们考虑在有限域中具有二次产生的化学排斥模型。首先，我们获得时间弱的全局解，并给出一个正则性准则（满足$\mathrm{1个}d$ 和 $2d$域）来推断唯一性和全局规律性。之后，我们研究了两个守恒和无条件能量稳定的一阶时间方案：（非线性和正向）Backward Euler方案和线性耦合版本，证明了可解性，收敛于弱解和误差估计。特别地，线性方案不能保持正性，并且非线性方案的唯一性在相对于离散解的强范数假设较小的时间步长的情况下得到了证明。这个假设减少到很小的时间$ñd$ 域（$ñ\le 2$）在全球范围内得到了强有力的估计。最后，我们通过一些数值模拟显示了方案的行为。