Abstract
In this paper we study a stationary chemo-repulsion model and analyze a related optimal bilinear control problem. We prove the existence of strong solutions of the state equations with a non-smooth source term in the chemical concentration equation, in bounded domains of \(\mathbb {R}^N,\) \(N=1,2,3,\) for any given mass, which permit us to consider optimal bilinear control problems. We prove the existence of optimal solutions and, by using a Lagrange multipliers theorem in Banach spaces, we obtain some first-order optimality conditions.
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Acknowledgements
S. Lorca has been supported by Proyecto UTA-Mayor 4744-19, Universidad de Tarapacá, Chile. E. Mallea-Zepeda has been supported by ANID-Chile through of project research Fondecyt de Iniciación 11200208. E.J. Villamizar-Roa has been supported by the Vicerrectoría de Investigación y Extensión of the Universidad Industrial de Santander, Proyecto 3704 (2022). Also, the authors would like to thank the anonymous referees for their kind and helpful remarks and comments.
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Lorca, S., Mallea-Zepeda, E. & Villamizar-Roa, É.J. Stationary Solutions to a Chemo-repulsion System and a Related Optimal Bilinear Control Problem. Bull Braz Math Soc, New Series 54, 39 (2023). https://doi.org/10.1007/s00574-023-00356-6
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DOI: https://doi.org/10.1007/s00574-023-00356-6