Article dans une revue
Titre :
Boundary feedback stabilization of two-dimensianal shallow water equations with viscosity term
Auteurs :
Ben Mansour Dia, Mouhamadou Samsidy Goudiaby, Olivier Dom
Résumé :
This paper treats a water flow regularization problem by means of local boundary condi- tions for the two-dimensional viscous shallow water equations. Using an a-priori energy estimate of the perturbation state and the Faedo–Galerkin method, we build a stabilizing boundary feedback control law for the volumetric flow in a finite time that is prescribed by the solvability of the associated Cauchy problem. We iterate the same approach to build by cascade a stabilizing feedback control law for infinite time. Thanks to a positive arbitrary time-dependent stabilization function, the control law provides an exponential decay of the energy.
Journal :
Mathematics
Volume :
10
Pages ou Numéro article :
4036
Année :
2022
DOI :
https://doi.org/10.3390/ math10214036
Date de publication :
31 October 2022
Lien de la publication :
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