Boundary stabilization of quasilinear hyperbolic systems of balance laws: Exponential decay for small source terms - Archive ouverte HAL Access content directly
Journal Articles Journal of Evolution Equations Year : 2018

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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Dates and versions

hal-01593773 , version 1 (26-09-2017)

Identifiers

  • HAL Id : hal-01593773 , version 1

Cite

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, 2018, 18 (3), pp.1471-1500. ⟨hal-01593773⟩
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