Finite-time stabilization in optimal time of homogeneous quasilinear hyperbolic systems in one dimensional space

Coron, Jean-Michel; Nguyen, Hoai-Minh

ESAIM: Control, Optimisation and Calculus of Variations, Tome 26 (2020), article no. 119

Suite au passage du modèle économique de la revue en S20, le texte intégral des articles des années 2019 et 2020 est accessible uniquement sur le site de l'éditeur et est réservé aux abonnés.

We consider the finite-time stabilization of homogeneous quasilinear hyperbolic systems with one side controls and with nonlinear boundary condition at the other side. We present time-independent feedbacks leading to the finite-time stabilization in any time larger than the optimal time for the null controllability of the linearized system if the initial condition is sufficiently small. One of the key technical points is to establish the local well-posedness of quasilinear hyperbolic systems with nonlinear, non-local boundary conditions.

Classification : 93D15, 35L50, 35L60
Keywords: Stabilization, nonlinear 1-D hyperbolic systems, feedback laws

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