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In this paper, we first introduce an abstract viscous hyperbolic problem for which we prove exponential decay under appropriated assumptions. We then give some illustrative examples, like the linearized viscous Saint-Venant system. In order to achieve the optimal decay rate, we also perform a detailed spectral analysis of our abstract problem under a natural assumption satisfied by various examples. We finally consider the boundary stabilizability of the linearized viscous Saint-Venant system on trees.
Nicaise, Serge 1
@article{COCV_2019__25__A33_0,
author = {Nicaise, Serge},
title = {Stability results of some first order viscous hyperbolic systems},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
publisher = {EDP-Sciences},
volume = {25},
year = {2019},
doi = {10.1051/cocv/2018020},
zbl = {1441.35055},
mrnumber = {4001033},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv/2018020/}
}
TY - JOUR AU - Nicaise, Serge TI - Stability results of some first order viscous hyperbolic systems JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2019 VL - 25 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/cocv/2018020/ DO - 10.1051/cocv/2018020 LA - en ID - COCV_2019__25__A33_0 ER -
%0 Journal Article %A Nicaise, Serge %T Stability results of some first order viscous hyperbolic systems %J ESAIM: Control, Optimisation and Calculus of Variations %D 2019 %V 25 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/cocv/2018020/ %R 10.1051/cocv/2018020 %G en %F COCV_2019__25__A33_0
Nicaise, Serge. Stability results of some first order viscous hyperbolic systems. ESAIM: Control, Optimisation and Calculus of Variations, Tome 25 (2019), article no. 33. doi : 10.1051/cocv/2018020. http://geodesic.mathdoc.fr/articles/10.1051/cocv/2018020/
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