Bilinear optimal control for weak solutions of the Keller-Segel logistic model in $2D$ domains
Optimization and Control
2022-07-01 v1 Analysis of PDEs
Abstract
An optimal control problem associated to the Keller-Segel with logistic reaction system will be studied in 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 and the chemical concentration ) 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).
Keywords
Cite
@article{arxiv.2206.15111,
title = {Bilinear optimal control for weak solutions of the Keller-Segel logistic model in $2D$ domains},
author = {P. Braz e Silva and F. Guillén-González and C. F. Perusato and M. A. Rodríguez-Bellido},
journal= {arXiv preprint arXiv:2206.15111},
year = {2022}
}
Comments
22 pages. arXiv admin note: text overlap with arXiv:1808.09294