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Hyperbolic systems in one dimensional space are frequently used in modelingof many physical systems. In our recent works, we introduced time independentfeedbacks leading to the finite stabilization for the optimal time ofhomogeneous linear and quasilinear hyperbolic systems. In this work, we presentLyapunov's functions for these feedbacks and use estimates for Lyapunov'sfunctions to rediscover the finite stabilization results.

Lyapunov functions and finite time stabilization in optimal time for homogeneous linear and quasilinear hyperbolic systems