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Asymptotic stability of the multidimensional wave equation coupled with classes of positive-real impedance boundary conditions

Monteghetti, Florian and Haine, Ghislain and Matignon, Denis Asymptotic stability of the multidimensional wave equation coupled with classes of positive-real impedance boundary conditions. (2019) Mathematical Control & Related Fields, 9 (4). 759-791. ISSN 2156-8499

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Official URL: https://doi.org/10.3934/mcrf.2019049

Abstract

This paper proves the asymptotic stability of the multidimensional wave equation posed on a bounded open Lipschitz set, coupled with various classes of positive-real impedance boundary conditions, chosen for their physical relevance: time-delayed, standard diffusive (which includes the Riemann-Liouville fractional integral) and extended diffusive (which includes the Caputo fractional derivative). The method of proof consists in formulating an abstract Cauchy problem on an extended state space using a dissipative realization of the impedance operator, be it finite or infinite-dimensional. The asymptotic stability of the corresponding strongly continuous semigroup is then obtained by verifying the sufficient spectral conditions derived by Arendt and Batty (Trans. Amer. Math. Soc., 306 (1988)) as well as Lyubich and Vũ (Studia Math., 88 (1988)).

Item Type:Article
HAL Id:hal-02362852
Audience (journal):International peer-reviewed journal
Uncontrolled Keywords:
Institution:French research institutions > Institut National de la Recherche en Informatique et en Automatique - INRIA (FRANCE)
Université de Toulouse > Institut Supérieur de l'Aéronautique et de l'Espace - ISAE-SUPAERO (FRANCE)
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Deposited By: Ghislain Haine
Deposited On:14 Nov 2019 08:55

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