Volume 8, 2002A tribute to JL Lions
|Page(s)||513 - 554|
|Published online||15 August 2002|
Local controllability of a 1-D tank containing a fluid modeled by the shallow water equations
Université Paris-Sud, Département de Mathématique,
bâtiment 425, 91405 Orsay, France; Jean-Michel.Coron@math.u-psud.fr.
We consider a 1-D tank containing an inviscid incompressible irrotational fluid. The tank is subject to the control which consists of horizontal moves. We assume that the motion of the fluid is well-described by the Saint–Venant equations (also called the shallow water equations). We prove the local controllability of this nonlinear control system around any steady state. As a corollary we get that one can move from any steady state to any other steady state.
Mathematics Subject Classification: 76B75 / 93B05 / 76B15 / 35F30
Key words: Controllability / hyperbolic systems / shallow water.
© EDP Sciences, SMAI, 2002
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.