Boundary stabilization of quasilinear hyperbolic systems of balance laws: 
Exponential decay for small source terms

Martin Gugat; Vincent Perrollaz; Lionel Rosier

Boundary stabilization of quasilinear hyperbolic systems of balance laws: Exponential decay for small source terms

Martin Gugat ¹ Vincent Perrollaz ² Lionel Rosier ^{3, 4}

1 FAU - Friedrich-Alexander Universität Erlangen-Nürnberg

2 LMPT - Laboratoire de Mathématiques et Physique Théorique

3 CAS - Centre Automatique et Systèmes

4 CAOR - Centre de Robotique

Abstract : We investigate the long-time behavior of solutions of quasilinear hyperbolic systems with transparent boundary conditions when small source terms are incorporated in the system. Even if the finite-time stability of the system is not preserved, it is shown here that an exponential convergence towards the steady state still holds with a decay rate which is proportional to the logarithm of the amplitude of the source term. The result is stated for a system with dynamical boundary conditions in order to deal with initial data that are free of any compatibility condition.

Keywords : telegraph equation finite-time stability System of balance laws shallow water equations dynamical boundary conditions exponential stability decay rate

Document type :

Journal articles

Domain :

Mathematics [math] / Analysis of PDEs [math.AP]

Engineering Sciences [physics] / Automatic

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Submitted on : Tuesday, September 26, 2017 - 4:30:40 PM
Last modification on : Thursday, December 20, 2018 - 10:22:03 PM
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Boundary stabilization of quasilinear hyperbolic systems of balance laws: Exponential decay for small source terms

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