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

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.
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Pré-publication, Document de travail
2017
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Dernière modification le : mardi 13 novembre 2018 - 01:15:35
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  • HAL Id : hal-01593773, version 1

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Martin Gugat, Vincent Perrollaz, Lionel Rosier. Boundary stabilization of quasilinear hyperbolic systems of balance laws: Exponential decay for small source terms. 2017. 〈hal-01593773〉

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