Volume 25, 2019
|Number of page(s)||38|
|Published online||09 September 2019|
Stability results of some first order viscous hyperbolic systems
Univ. Valenciennes, EA 4015 – LAMAV – Laboratoire de Mathématiques et leurs Applications de Valenciennes,
FR CNRS 2956,
* Corresponding author: firstname.lastname@example.org
Accepted: 10 March 2018
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.
Mathematics Subject Classification: 35L50 / 93D15 / 35B37
Key words: Hyperbolic systems / viscosity / stabilization
© The author. Published by EDP Sciences, SMAI 2019
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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