| Issue |
ESAIM: COCV
Volume 11, Number 3, July 2005
|
|
|---|---|---|
| Page(s) | 487 - 507 | |
| DOI | https://doi.org/10.1051/cocv:2005016 | |
| Published online | 15 July 2005 | |
Asymptotic stability of linear conservative systems when coupled with diffusive systems
1
Télécom Paris, dépt TSI
& CNRS, UMR 5141, 37-39 rue Dareau, 75 014 Paris, France;
matignon@tsi.enst.fr
2
LAAS - CNRS,
7 avenue du Colonel Roche 31077 Toulouse, France;
prieur@laas.fr
Received:
16
March
2004
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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