Feedback stabilization of a simplified model of fluid–structure interaction on a tree

Article type: Research Article

Authors: Ammari, Kaïs^{a; *} | Shel, Farhat^a | Vanninathan, Muthusamy^{b; c}

Affiliations: [a] UR Analysis and Control of PDEs, UR 13ES64, Department of Mathematics, Faculty of Sciences of Monastir, University of Monastir, Monastir, Tunisia. E-mails: kais.ammari@fsm.rnu.tn, farhat.shel@ipeit.rnu.tn | [b] TIFR-CAM, Post Bag 6503, Bangalore 560065, India | [c] Mathematics Department, IIT-Bombay, Mumbai, 400076, India. E-mail: vanni@math.tifrbng.res.in

Correspondence: [*] Corresponding author. E-mail: kais.ammari@fsm.rnu.tn.

Abstract: In this paper we study the dynamic feedback stability for some simplified model of fluid–structure interaction on a tree. We prove that, under some conditions, the energy of the solutions of the dissipative system decay exponentially to zero when the time tends to infinity. Our technique is based on a frequency domain method and a special analysis for the resolvent.

Keywords: Dynamic feedback, asymptotic stabilization, resolvent method

DOI: 10.3233/ASY-171418

Journal: Asymptotic Analysis, vol. 103, no. 1-2, pp. 33-55, 2017