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Article Dans Une Revue ESAIM: Control, Optimisation and Calculus of Variations Année : 2005

Asymptotic stability of linear conservative systems when coupled with diffusive systems

Résumé

In this paper we study linear conservative systems of finite dimension coupled with an infinite dimensional system of diffusive type. Computing the time-derivative of an appropriate energy functional along the solutions helps us to prove the well-posedness of the system and a stability property. But in order to prove asymptotic stability we need to apply a sufficient spectral condition. We also illustrate the sharpness of this condition by exhibiting some systems for which we do not have the asymptotic property.
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hal-03599604 , version 1 (07-03-2022)

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Denis Matignon, Christophe Prieur. Asymptotic stability of linear conservative systems when coupled with diffusive systems. ESAIM: Control, Optimisation and Calculus of Variations, 2005, 11 (3), pp.487-507. ⟨10.1051/cocv:2005016⟩. ⟨hal-03599604⟩
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