SU, Pei; TUCSNAK, Marius

doi:10.3934/mcrf.2022048

Métadonnées

Afficher la notice complète

Licence d’utilisation du document

SU, Pei
Institut de Mathématiques de Bordeaux [IMB]

TUCSNAK, Marius
Institut de Mathématiques de Bordeaux [IMB]

Langue

Article de revue

Ce document a été publié dans

Mathematical Control and Related Fields. 2022-10-20

AIMS

Date de soutenance

2022-10-20

Résumé en anglais

We consider a control system describing the interaction of water waves with a partially immersed rigid body constraint to move only in the vertical direction. The fluid is modeled by the shallow water equations. The control signal is a vertical force acting on the floating body. We first derive the full governing equations of the fluid-body system in a water tank and reformulate them as an initial boundary value problem of a first-order evolution system. We then linearize the equations around the equilibrium state and we study its well-posedness. Finally we focus on the reachability and stabilizability of the linear system. Our main result asserts that, provided that the floating body is situated in the middle of the tank, any symmetric waves with appropriate regularity can be obtained from the equilibrium state by an appropriate control force. This implies, in particular, that we can project this system on the subspace of states with appropriate symmetry properties to obtain a reduced system which is approximately controllable and strongly stabilizable. Note that, in general, this system is not controllable (even approximately).< Réduire

Mots clés en anglais

Shallow water equations

fluid-structure interactions

reachability

stabilizability

operator semigroup

infinite dimensional system

URI

https://oskar-bordeaux.fr/handle/20.500.12278/191512

DOI

http://dx.doi.org/10.3934/mcrf.2022048

Project ANR

Ecoulements avec singularités : couches limites, filaments de vortex, interaction vague-structure - ANR-18-CE40-0027

Origine

Importé de hal

Unités de recherche

Institut de Mathématiques de Bordeaux (IMB) - UMR 5251