Stability of an abstract-wave equation with delay and a Kelvin–Voigt damping

Article type: Research Article

Authors: Ammari, Kaïs^{a; *} | Nicaise, Serge^b | Pignotti, Cristina^c

Affiliations: [a] UR Analysis and Control of Pde, UR 13ES64, Department of Mathematics, Faculty of Sciences of Monastir, University of Monastir, Monastir, Tunisia | [b] LAMAV, FR CNRS 2956, Université de Valenciennes et du Hainaut Cambrésis, Valenciennes Cedex, France | [c] Dipartimento di Ingegneria e Scienze dell’Informazione e Matematica, Università di L’Aquila, L’Aquila, Italy

Correspondence: [*] Corresponding author: Kaïs Ammari, UR Analysis and Control of Pde, UR 13ES64, Department of Mathematics, Faculty of Sciences of Monastir, University of Monastir, 5019 Monastir, Tunisia. E-mail: [email protected].

Abstract: In this paper we consider a stabilization problem for an abstract wave equation with delay and a Kelvin–Voigt damping. We prove an exponential stability result for appropriate damping coefficients. The proof of the main result is based on a frequency-domain approach.

Keywords: internal stabilization, Kelvin–Voigt damping, abstract wave equation with delay

DOI: 10.3233/ASY-151317

Journal: Asymptotic Analysis, vol. 95, no. 1-2, pp. 21-38, 2015