Dissipative boundary conditions for one-dimensional quasi-linear hyperbolic systems: Lyapunov stability for the {$C^1$}-norm

International audienceThis paper is concerned with boundary dissipative conditions that guarantee the exponential stability of classical solutions of one-dimensional quasi-linear hyperbolic systems. We present a comprehensive review of the results that are available in the literature. The main result of the paper is then to supplement these previous results by showing how a new Lyapunov stability approach can be used for the analysis of boundary conditions that are known to be dissipative for the C1-norm