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Boundary stabilization of quasilinear hyperbolic systems of balance laws: Exponential decay for small source terms (1709.09893v1)
Published 28 Sep 2017 in math.AP
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.