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@article{faucris.107392824,
abstract = {For a system that is governed by the isothermal Euler equations with friction for ideal gas, the corresponding field of characteristic curves is determined by the velocity of the flow. This velocity is determined by a second-order quasilinear hyperbolic equation. For the corresponding initial-boundary value problem with Neumann-boundary feedback, we consider non-stationary solutions locally around a stationary state on a finite time interval and discuss the well-posedness of this kind of problem. We introduce a strict H-2-Lyapunov function and show that the boundary feedback constant can be chosen such that the H-2-Lyapunov function and hence also the H-2-norm of the difference between the non-stationary and the stationary state decays exponentially with time.},
author = {Leugering, Günter and Gugat, Martin and Wang, Ke},
doi = {10.3934/mcrf.2017015},
faupublication = {yes},
journal = {Mathematical Control and Related Fields},
keywords = {Boundary feedback control;feedback stabilization;exponential stability;isothermal Euler equations;second-order quasilinear equation;Lyapunov function;stationary state;non-stationary state;gas pipeline},
pages = {419-448},
peerreviewed = {Yes},
title = {{NEUMANN} {BOUNDARY} {FEEDBACK} {STABILIZATION} {FOR} {A} {NONLINEAR} {WAVE} {EQUATION}: {A} {STRICT} {H}-2-{LYAPUNOV} {FUNCTION}},
volume = {7},
year = {2017}
}