Remarks on global controllability for the shallow-water system with two control forces

Haspot, Boris; Drici, Abdelmalek

Haspot, Boris; Drici, Abdelmalek (2012), Remarks on global controllability for the shallow-water system with two control forces. https://basepub.dauphine.fr/handle/123456789/8226

Type

Document de travail / Working paper

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http://hal.archives-ouvertes.fr/hal-00666437

Date

2012

Éditeur

Université Paris-Dauphine

Ville d’édition

Paris

Métadonnées

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Auteur(s)

Haspot, Boris
Drici, Abdelmalek

Résumé (EN)

In this paper we deal with the compressible Navier-Stokes equations with a friction term in one dimension on an interval. We study the exact controllability properties of this equation with general initial condition when the boundary control is acting at both endpoints of the interval. Inspired by the work of Guerrero and Imanuvilov in \cite{GI} on the viscous Burger equation, we prove by choosing irrotational data and using the notion of effective velocity developed in \cite{cpde,cras} that the exact global controllability result does not hold for any time $T$.

Mots-clés

Control theory; Analysis of PDE