Geodesic
Asymptotic stability of linear conservative systems when coupled with diffusive systems
ESAIM: Control, Optimisation and Calculus of Variations, Tome 11 (2005) no. 3, pp. 487-507

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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.

DOI : 10.1051/cocv:2005016
Classification : 35B37, 93C20, 93D20
Keywords: asymptotic stability, well-posed systems, Lyapunov functional, diffusive representation, fractional calculus 
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     title = {Asymptotic stability of linear conservative systems when coupled with diffusive systems},
     journal = {ESAIM: Control, Optimisation and Calculus of Variations},
     pages = {487--507},
     publisher = {EDP-Sciences},
     volume = {11},
     number = {3},
     year = {2005},
     doi = {10.1051/cocv:2005016},
     mrnumber = {2148855},
     zbl = {1125.93030},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv:2005016/}
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Matignon, Denis; Prieur, Christophe. Asymptotic stability of linear conservative systems when coupled with diffusive systems. ESAIM: Control, Optimisation and Calculus of Variations, Tome 11 (2005) no. 3, pp. 487-507. doi: 10.1051/cocv:2005016

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