# American Institute of Mathematical Sciences

June  2013, 2(2): 379-402. doi: 10.3934/eect.2013.2.379

## Controllability of a 1-D tank containing a fluid modeled by a Boussinesq system

 1 Instituto de Matemática, Universidade Federal do Rio de Janeiro, P.O. Box 68530, CEP 21941-909, Rio de Janeiro, RJ, Brazil 2 Institut Elie Cartan de Lorraine, UMR 7502 UdL/CNRS/INRIA, B.P. 70239, F-54506 Vandœuvre-lès-Nancy Cedex, France

Received  September 2012 Revised  February 2013 Published  March 2013

This paper is concerned with the exact controllability problem for a 1-D tank containing an inviscid incompressible irrotational fluid. The tank is subject to one-dimensional horizontal motion. We take as fluid model a Boussinesq system of KdV-KdV type, and as control the acceleration of the tank. We derive for the linearized system an exact controllability result in small time in an appropriate space.
Citation: Dugan Nina, Ademir Fernando Pazoto, Lionel Rosier. Controllability of a 1-D tank containing a fluid modeled by a Boussinesq system. Evolution Equations & Control Theory, 2013, 2 (2) : 379-402. doi: 10.3934/eect.2013.2.379
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