Volume 26, 2020
Special issue in the honor of Enrique Zuazua's 60th birthday
|Number of page(s)||24|
|Published online||17 December 2020|
Finite-time stabilization in optimal time of homogeneous quasilinear hyperbolic systems in one dimensional space*
Sorbonne Université, Université de Paris, CNRS, INRIA, Laboratoire Jacques-Louis Lions, équipe Cage,
2 Ecole Polytechnique Fédérale de Lausanne, EPFL, CAMA, Station 8, CH-1015 Lausanne, Switzerland.
** Corresponding author: firstname.lastname@example.org
Accepted: 22 September 2020
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.
Mathematics Subject Classification: 93D15 / 35L50 / 35L60
Key words: Stabilization / nonlinear 1-D hyperbolic systems / feedback laws
© The authors. Published by EDP Sciences, SMAI 2020
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