SIAM Journal on Control and Optimization, Volume 58, Issue 3, Page 1457-1490, January 2020.
In this paper, a bilinear optimal control problem associated to a 3D chemo-repulsion model with linear production is studied. The existence of weak solutions is proved, and a regularity criterion to get global-in-time strong solutions is established. As a consequence, the existence of a global optimal solution with bilinear control is deduced, and using a Lagrange multiplier theorem, first-order optimality conditions for local optimal solutions are derived.

中文翻译：

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3D化学排斥系统的正则判据及其在双线性最优控制问题中的应用

SIAM控制与优化杂志，第58卷，第3期，第1457-1490页，2020
年1月。在本文中，研究了与线性生产的3D化学排斥模型相关的双线性最优控制问题。证明了弱解的存在性，并建立了获得全局及时强解的规则性准则。结果，推导了具有双线性控制的全局最优解的存在，并使用拉格朗日乘子定理，得出了局部最优解的一阶最优性条件。