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.

Classification: 35B37, 93C20, 93D20

Keywords: asymptotic stability, well-posed systems, Lyapunov functional, diffusive representation, fractional calculus

@article{COCV_2005__11_3_487_0, author = {Matignon, Denis and Prieur, Christophe}, title = {Asymptotic stability of linear conservative systems when coupled with diffusive systems}, journal = {ESAIM: Control, Optimisation and Calculus of Variations}, publisher = {EDP-Sciences}, volume = {11}, number = {3}, year = {2005}, pages = {487-507}, doi = {10.1051/cocv:2005016}, zbl = {1125.93030}, mrnumber = {2148855}, language = {en}, url = {http://www.numdam.org/item/COCV_2005__11_3_487_0} }

Matignon, Denis; Prieur, Christophe. Asymptotic stability of linear conservative systems when coupled with diffusive systems. ESAIM: Control, Optimisation and Calculus of Variations, Volume 11 (2005) no. 3, pp. 487-507. doi : 10.1051/cocv:2005016. http://www.numdam.org/item/COCV_2005__11_3_487_0/

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