In this paper we study a stationary chemo-repulsion model and analyze a related optimal bilinear control problem. We prove the existence of strong solutions of the state equations with a non-smooth source term in the chemical concentration equation, in bounded domains of \(\mathbb {R}^N,\) \(N=1,2,3,\) for any given mass, which permit us to consider optimal bilinear control problems. We prove the existence of optimal solutions and, by using a Lagrange multipliers theorem in Banach spaces, we obtain some first-order optimality conditions.

中文翻译：

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化学排斥系统的稳态解及相关的最优双线性控制问题

在本文中，我们研究了稳态化学排斥模型并分析了相关的最优双线性控制问题。我们证明了化学浓度方程中具有非光滑源项的状态方程在\(\mathbb {R}^N,\) \(N=1,2,3, \)对于任何给定的质量，这使我们能够考虑最优双线性控制问题。我们证明了最优解的存在性，并通过在 Banach 空间中使用拉格朗日乘数定理，我们获得了一些一阶最优性条件。