Volume 11, Number 3, July 2005
|Page(s)||487 - 507|
|Published online||15 July 2005|
Asymptotic stability of linear conservative systems when coupled with diffusive systems
Télécom Paris, dépt TSI
& CNRS, UMR 5141, 37-39 rue Dareau, 75 014 Paris, France;
2 LAAS - CNRS, 7 avenue du Colonel Roche 31077 Toulouse, France; firstname.lastname@example.org
Revised: 21 October 2004
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.
Mathematics Subject Classification: 35B37 / 93C20 / 93D20
Key words: Asymptotic stability / well-posed systems / Lyapunov functional / diffusive representation / fractional calculus.
© EDP Sciences, SMAI, 2005
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