Null controllability in a fluid–solid structure model☆

A model representing a coupling between a heat conducting medium and a solid structure is considered. We establish a Carleman inequality for this model. Next we deduce a null controllability result with an internal control in the conducting medium and there is no control in the solid part.

[1]  E. Fernández-Cara,et al.  Global Carleman estimates for solutions of parabolic systems defined by transposition and some applications to controllability , 2006 .

[2]  Sergio Guerrero,et al.  LOCAL EXACT CONTROLLABILITY TO THE TRAJECTORIES OF THE BOUSSINESQ SYSTEM VIA A FICTITIOUS CONTROL ON THE DIVERGENCE EQUATION , 2008 .

[3]  Sergio Guerrero,et al.  Global Carleman Inequalities for Parabolic Systems and Applications to Controllability , 2006, SIAM J. Control. Optim..

[4]  J. Puel,et al.  Global Carleman estimates for weak solutions of elliptic nonhomogeneous Dirichlet problems , 2002 .

[5]  Jean-Pierre Raymond,et al.  Null-controllability for a Coupled Heat-Finite-dimensional Beam System , 2009 .

[6]  Axel Osses,et al.  Local null controllability of a two-dimensional fluid-structure interaction problem , 2008 .

[7]  C. Conca,et al.  Fluids And Periodic Structures , 1995 .

[8]  Oleg Yu. Imanuvilov,et al.  Exact controllability of a fluid-rigid body system , 2007 .

[9]  D. L. Russell.  Review: J.-L. Lions, Controlabilité Exacte, Perturbations et Stabilisation de Systèmes Distribués , 1990 .

[10]  O Yu Emanuilov,et al.  Controllability of parabolic equations , 1995 .

[11]  Sergio Guerrero,et al.  Local exact controllability of the Navier-Stokes system ✩ , 2004 .

[12]  G. Lebeau,et al.  RÉGULARITÉ ET UNICITÉ POUR LE PROBLÈME DE STOKES , 2002 .

[13]  Jean-Claude Saut,et al.  Unique continuation for some evolution equations , 1987 .

[14]  A. Fursikov.  Optimal Control of Distributed Systems: Theory and Applications , 2000 .

[15]  Jean-Pierre Raymond,et al.  Stokes and Navier-Stokes equations with a nonhomogeneous divergence condition , 2010 .

[16]  Jean-Pierre Raymond,et al.  Exact controllability in fluid – solid structure: The Helmholtz model , 2005 .

[17]  Oleg Yu. Imanuvilov,et al.  Controllability of Evolution equations , 1996 .

[18]  C. Fabre,et al.  Prolongement Unique Des Solutions , 1996 .

[19]  R. Farwig,et al.  Very weak, weak and strong solutions to the instationary Navier-Stokes system , 2007 .

[20]  Jean-Pierre Raymond,et al.  Stokes and Navier-Stokes equations with nonhomogeneous boundary conditions , 2007 .

[21]  Jacques-Louis Lions.  Contrôlabilite exacte et homogénéisation (I) , 1988 .

[22]  A. V. Fursikov,et al.  Optimal control of distributed systems , 1999 .

[23]  Giovanni P. Galdi,et al.  An Introduction to the Mathematical Theory of the Navier-Stokes Equations: Steady-State Problems , 2011 .

[24]  Jean-Pierre Raymond,et al.  Null Controllability in a Heat–Solid Structure Model , 2009 .

[25]  E. Fernández-Caraa,et al.  Local exact controllability of the Navier – Stokes system ✩ , 2004 .