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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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Submitted on : Tuesday, September 26, 2017 - 4:30:40 PM
Last modification on : Tuesday, January 11, 2022 - 5:56:09 PM
Long-term archiving on: : Wednesday, December 27, 2017 - 1:52:57 PM

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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. Journal of Evolution Equations, Springer Verlag, 2018, 18 (3), pp.1471-1500. ⟨hal-01593773⟩

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