A uniform controllability result for the Keller–Segel system

Article type: Research Article

Authors: Chaves-Silva, Felipe Wallison^; | Guerrero, Sergio

Affiliations: BCAM-Basque Center for Applied Mathematics, Bilbao, Basque Country, Spain. E-mail: felipewallison@gmail.com | Université Pierre et Marie Curie-Paris 6, UMR 7598 Laboratoire Jacques-Louis Lions, Paris, France. E-mail: guerrero@ann.jussieu.fr

Note: [] Corresponding author: Felipe Wallison Chaves-Silva, BCAM-Basque Center for Applied Mathematics, Mazarredo 14, 48009 Bilbao, Basque Country, Spain. E-mail: E-mail: felipewallison@gmail.com

Abstract: In this paper we study the controllability of the Keller–Segel system approximating its parabolic–elliptic version. We show that this parabolic system is locally uniform controllable around a constant solution of the parabolic–elliptic system when the control is acting on the component of the chemical.

Keywords: Keller–Segel system, controllability to trajectories, Carleman estimates

DOI: 10.3233/ASY-141282

Journal: Asymptotic Analysis, vol. 92, no. 3-4, pp. 313-338, 2015