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

Martin Gugat; Vincent Perrollaz; Lionel Rosier

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arXiv · 1709.09893

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

Martin Gugat·Vincent Perrollaz·Lionel Rosier

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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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Martin Gugat, Vincent Perrollaz, Lionel Rosier. 2017-09-28. Boundary stabilization of quasilinear hyperbolic systems of balance laws: Exponential decay for small source terms. https://arxiv.org/abs/1709.09893

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