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

Dugan Nina; Ademir Fernando Pazoto; Lionel Rosier

doi:10.3934/eect.2013.2.379

Article Contents

2013, Volume 2, Issue 2: 379-402. Doi: 10.3934/eect.2013.2.379

This issue Previous Article Global well-posedness and exponential stability for Kuznetsov's equation in $L_p$-spaces Next Article Nonlinear instability of solutions in parabolic and hyperbolic diffusion

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
2.
Institut Elie Cartan de Lorraine, UMR 7502 UdL/CNRS/INRIA, B.P. 70239, F-54506 Vandœuvre-lès-Nancy Cedex

Received: September 2012

Revised: February 2013

Published: June 2013

Abstract / Introduction Related Papers Cited by

Abstract

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.

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Mathematics Subject Classification: Primary: 93B05, 35Q53; Secondary: 93C20.

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