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arXiv · 2206.15111

Bilinear optimal control for weak solutions of the Keller-Segel logistic model in $2D$ domains

P. Braz e Silva·F. Guillén-González·C. F. Perusato·M. A. Rodríguez-Bellido
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Abstract

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. Guill\'en-Gonz\'alez et al. ESAIM Control Optim. Calc. Var. 26 (2020), Paper No. 29, 21 pp).

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P. Braz e Silva, F. Guillén-González, C. F. Perusato, M. A. Rodríguez-Bellido. 2022-06-30. Bilinear optimal control for weak solutions of the Keller-Segel logistic model in $2D$ domains. https://arxiv.org/abs/2206.15111

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