三维化学排斥系统的正则性判据及其在双线性最优控制问题中的应用
A regularity criterion for a 3D chemo-repulsion system and its application to a bilinear optimal control problem
摘要：
本文研究了一类具有线性生产的三维化学排斥模型的双线性最优控制问题。我们证明了弱解的存在性，并建立了一个正则性准则来得到整体时间强解。因此，我们推导出一个全局最优解的存在性与双线性控制，并使用拉格朗日乘子定理，我们推导出一阶最优性条件的局部最优解。
英文摘要：
In this paper we study a bilinear optimal control problem associated to a 3D chemo-repulsion model with linear production. We prove the existence of weak solutions and we establish a regularity criterion to get global in time strong solutions. As a consequence, we deduce the existence of a global optimal solution with bilinear control and, using a Lagrange multipliers theorem, we derive first-order optimality conditions for local optimal solutions.
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