@article{AIHPC_2008__25_2_219_0, author = {Horsin, Thierry}, title = {Local exact lagrangian controllability of the {Burgers} viscous equation}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, pages = {219--230}, publisher = {Elsevier}, volume = {25}, number = {2}, year = {2008}, doi = {10.1016/j.anihpc.2006.11.009}, mrnumber = {2396520}, zbl = {1145.35330}, language = {en}, url = {http://www.numdam.org/articles/10.1016/j.anihpc.2006.11.009/} }
TY - JOUR AU - Horsin, Thierry TI - Local exact lagrangian controllability of the Burgers viscous equation JO - Annales de l'I.H.P. Analyse non linéaire PY - 2008 SP - 219 EP - 230 VL - 25 IS - 2 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.anihpc.2006.11.009/ DO - 10.1016/j.anihpc.2006.11.009 LA - en ID - AIHPC_2008__25_2_219_0 ER -
%0 Journal Article %A Horsin, Thierry %T Local exact lagrangian controllability of the Burgers viscous equation %J Annales de l'I.H.P. Analyse non linéaire %D 2008 %P 219-230 %V 25 %N 2 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.anihpc.2006.11.009/ %R 10.1016/j.anihpc.2006.11.009 %G en %F AIHPC_2008__25_2_219_0
Horsin, Thierry. Local exact lagrangian controllability of the Burgers viscous equation. Annales de l'I.H.P. Analyse non linéaire, Tome 25 (2008) no. 2, pp. 219-230. doi : 10.1016/j.anihpc.2006.11.009. http://www.numdam.org/articles/10.1016/j.anihpc.2006.11.009/
[1] On the attainable set for scalar nonlinear conservation laws with boundary control, SIAM J. Control Optim. 36 (1) (1998) 290-312. | MR | Zbl
, ,[2] Two-dimensional local null controllability of a rigid structure in a Navier-Stokes fluid, C. R. Acad. Sci. Paris, Ser. I 343 (2) (2006) 105-109. | MR | Zbl
, ,[3] H. Brezis, T. Cazenave, Semilinear Evolution Equations and Applications in Mechanics and Physics, Pitman Lecture Notes, Addison-Wesley, Reading MA, in press.
[4] Theory of Ordinary Differential Equations, McGraw-Hill Book Company, New York, 1955. | MR | Zbl
, ,[5] Existence of solutions for the equations modelling the motion of a rigid body in a viscous fluid, Comm. Partial Differential Equations 25 (5-6) (2000) 1019-1042. | MR | Zbl
, , ,[6] J.-M. Coron, Control and nonlinearity, in preparation. | Zbl
[7] Contrôlabilité exacte frontière de l'équation d'Euler des fluides parfaits incompressibles bidimensionnels, C. R. Acad. Sci. Paris 317 (1993) 271-276. | MR | Zbl
,[8] On the controllability of the 2-D incompressible Navier-Stokes equations with the Navier slip boundary conditions, ESAIM Control Optim. Calc. Var. 1 (1995/1996) 35-75, (electronic). | Numdam | MR | Zbl
,[9] Local controllability of a 1-D tank containing a fluid modeled by the shallow water equations, ESAIM Control Optim. Calc. Var. 8 (2002) 513-554, A tribute to J.L. Lions. | Numdam | MR | Zbl
,[10] Global steady-state controllability of one-dimensional semilinear heat equations, SIAM J. Control Optim. 43 (2) (2004) 549-569, (electronic). | MR | Zbl
, ,[11] On weak solutions for fluid-rigid structure interaction: compressible and incompressible models, Comm. Partial Differential Equations 25 (7-8) (2000) 1399-1413. | MR | Zbl
, ,[12] Ordinary differential equations, transport theory and Sobolev spaces, Invent. Math. 98 (1989) 511-547. | MR | Zbl
, ,[13] Some control results for simplified one-dimensional models of fluid-solid interaction, Math. Models Methods Appl. Sci. 15 (5) (2005) 783-824. | MR | Zbl
, ,[14] Approximate controllability of the semilinear heat equation, Proc. Roy. Soc. Edinburgh Sect. A 125 (1) (1995) 31-61. | MR | Zbl
, , ,[15] Exact controllability theorems for linear parabolic equations in one space dimension, Arch. Rational Mech. Anal. 43 (1971) 272-292. | MR | Zbl
, ,[16] Remarks on the controllability of the Burgers equation, C. R. Acad. Sci. Paris, Ser. I 341 (2005) 229-232. | MR | Zbl
, ,[17] Local exact controllability of the Navier-Stokes system, J. Math. Pures Appl. (9) 83 (12) (2004) 1501-1542. | MR
, , , ,[18] Controllability of Evolution Equations, Lecture Notes Series, vol. 34, Seoul National University Research Institute of Mathematics, Global Analysis Research Center, Seoul, 1996. | MR | Zbl
, ,[19] Numerical Approximation of Hyperbolic Systems of Conservation Laws, Applied Mathematical Sciences, vol. 118, Springer-Verlag, New York, 1996. | MR | Zbl
, ,[20] S. Guerrero, O.Yu. Imanuvilov, Remarks on global controllability for the Burgers equation with two control forces (2006), submitted for publication. | Numdam | MR
[21] Lectures on Nonlinear Hyperbolic Differential Equations, Mathématiques & Applications (Berlin), vol. 26, Springer-Verlag, Berlin, 1997. | MR | Zbl
,[22] On the controllability of the Burgers equation, ESAIM Control Optim. Calc. Var. 3 (1998) 83-95, (electronic). | Numdam | MR | Zbl
,[23] Application of the exact null controllability of the heat equation to moving sets, C. R. Acad. Sci. Paris, Ser. I 342 (2006) 849-852. | MR | Zbl
,[24] On exact controllability for the Navier-Stokes equations, ESAIM Control Optim. Calc. Var. 3 (1998) 97-131, (electronic). | Numdam | MR | Zbl
,[25] Remarks on exact controllability for the Navier-Stokes equations, ESAIM Control Optim. Calc. Var. 6 (2001) 39-72, (electronic). | Numdam | MR | Zbl
,[26] Approximation of exact boundary controllability problems for the 1-D wave equation by optimization-based methods, in: Recent Advances in Scientific Computing and Partial Differential Equations, Hong Kong, 2002, Contemp. Math., vol. 330, Amer. Math. Soc., Providence, RI, 2003, pp. 133-153. | MR | Zbl
, , ,[27] Contrôle exact de l'équation de la chaleur, Comm. Partial Differential Equations 20 (1-2) (1995) 335-356. | MR | Zbl
, ,[28] H. Maillot, E. Zuazua, Mouvement d'une particule dans un fluide, Prepublication, 1999.
[29] Controllability of quantum harmonic oscillators, IEEE Trans. Automat. Control 49 (5) (2004) 745-747. | MR
, ,[30] Variational assimilation of Lagrangian data in oceanography, Inverse Problems 22 (1) (2006) 245-263. | MR | Zbl
,[31] A. Osses, Quelques méthodes théoriques et numériques de contrôlabilité et problèmes d'interactions fluide-structure, PhD thesis, Ecole Polytechnique, Paris, 1998.
[32] Deterministic finite-dimensional systems, in: Mathematical Control Theory, second ed., Texts in Applied Mathematics, vol. 6, Springer-Verlag, New York, 1998, pp. xvi+531. | MR | Zbl
,[33] Lack of collision in a simplified 1D model for fluid-solid interaction, Math. Models Methods Appl. Sci. 16 (5) (2006) 637-678. | MR
, ,Cité par Sources :