论文标题
凯勒 - 塞格逻辑模型$ 2D $域的弱解决方案的双线性最佳控制
Bilinear optimal control for weak solutions of the Keller-Segel logistic model in $2D$ domains
论文作者
论文摘要
将以$ 2D $域中研究与凯勒·塞格（Keller-Segel）相关的最佳控制问题。该控制仅在化学方程式中以双线性形式起作用。推导了最佳控制和必要的最优系统的存在。 主要的新颖性是，控制可能是相当奇异的，并且状态（细胞密度$ u $和化学浓度$ v $）仅在弱环境中，这在文献中并不是往常的解决最佳控制问题的最佳控制问题（例如，参见Guillén-González等人EsaimControl。EsaimControl。Cart。Calc。26（var。26（20202020202020202020202020202020202020202020202020202020202020202020202020年），纸质编号29，21 pp）。
An optimal control problem associated to the Keller-Segel with logistic reaction system will be studied in $2D$ domains. The control acts in a bilinear form only in the chemical equation. The existence of optimal control and a necessary optimality system are deduced. The main novelty is that control can be rather singular and the state (cell density $u$ and the chemical concentration $v$) remains only in a weak setting, which is not usual in the literature to solve optimal control problems subject to chemotaxis models (see e.g. Guillén-González et al. ESAIM Control Optim. Calc. Var. 26 (2020), Paper No. 29, 21 pp).
