Bilinear Optimal Control of the Keller–Segel Logistic Model in 2D-Domains

An optimal control problem associated to the Keller–Segel with logistic reaction system is studied in 2D domains. The control acts in a bilinear form only in the chemical equation. The existence of an optimal control and a necessary optimality system are deduced. The main novelty is that the control...

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Bibliographic Details
Published inApplied mathematics & optimization Vol. 87; no. 3; p. 55
Main Authors Braz e Silva, P., Guillén-González, F., Perusato, C. F., Rodríguez-Bellido, M. A.
Format Journal Article
LanguageEnglish
Published New York Springer US 01.06.2023
Springer Nature B.V
Subjects
Applied mathematics
Calculus of Variations and Optimal Control; Optimization
Control
Domains
Mathematical and Computational Physics
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
Numerical and Computational Physics
Optimal control
Optimization
Simulation
Systems Theory
Theoretical
Two dimensional models
Optimality conditions
35K51
Weak solutions
49K20
49J20
Chemotaxis model
Logistic reaction
Bilinear optimal control
35Q92
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Summary:An optimal control problem associated to the Keller–Segel with logistic reaction system is studied in 2D domains. The control acts in a bilinear form only in the chemical equation. The existence of an optimal control and a necessary optimality system are deduced. The main novelty is that the 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.
ISSN:0095-4616
1432-0606
DOI:10.1007/s00245-023-09988-y