Karine Beauchard  

Chargée de recherches au CNRS,
Professeur chargé de cours a l'école polytechnique,
Membre du CMLS.
Centre de Mathématiques Laurent Schwartz
École Polytechnique
91128 Palaiseau Cedex

Courriel : Karine.Beauchard-at-math.polytechnique.fr
Bureau : 6:10-09
Téléphone : +33169334941

CV au format pdf

THEMES DE RECHERCHES :

- analyse et contrôle d'EDP
- contrôle quantique : équation de Schrödinger, équation de Bloch
- contrôle d'équations paraboliques dégénérées de type hypoelliptique : équation de Grushin, équation de Kolmogorov, équation de Fokker Planck
- stabilisation
- problèmes inverses, observateurs asymptotiques

ARTICLES :


26) K. Beauchard, L. Miller and M. Morancey. 2D Grushin-type equations: minimal time and null controllable data (preprint) pdf
25) K. Beauchard, H. Lange and H. Teismann. Local exact controllability of a Bose-Einstein condensate in a 1D time-varying box. (submitted, arXiv:1303.2713) pdf
24) N. Zarrouati-Vissière, K. Beauchard and P. Rouchon. 6 Degree-of-Freedom motion estimation from depth images and magneto-inertial data for trajectory reconstruction (submitted) pdf
23) K. Beauchard, J.-M. Coron and H. Teismann. Minimal time for the bilinear control of Schrödinger equations, accepted in SCL, 2014 pdf
22) K. Beauchard, B. Helffer, R. Henry, L. Robbiano. Degenerate parabolic operators of Kolmogorov type with a geometric control condition, accepted in ESAIM:COCV, 2014 pdf
21) K. Beauchard, N. Zarrouati-Vissière and P. Rouchon. Rotational and translational bias estimation based on depth and image measurements. accepted in SICON, 2014 pdf
20) K. Beauchard, P. Cannarsa and M. Yamamotto. Inverse source problem and null controllability for multidimensional Grushin-type parabolic operators. Inverse Problems, Volume 30, Number 2, February 2014. pdf
19) K. Beauchard. Null controllability of Kolmogorov-type equations. Mathematics of Control, Signals, and Systems (MCSS), vol. 26, n. 1, p. 145-176, March 2014. pdf
18) K. Beauchard and M. Morancey. Local controllability of 1D Schrödinger equations with bilinear control and minimal time. Mathematical Control and Related Fields (MCRF), Vol. 4, No. 2, June 2014 pdf
17) K. Beauchard, P. Pereira da Silva and P. Rouchon. Stabilization of an arbitrary profile for an ensemble of half-spin systems. (to appear in Automatica) pdf
16) K. Beauchard, P. Cannarsa, R. Guglielmi. Null controllability of Grushin-type operators in dimension two, (to appear in JEMS) pdf
15) K. Beauchard, P. Pereira da Silva and P. Rouchon. Stabilization and motion planning for an ensemble of half spin system, Automatica 48, pp.68-76, 2012. pdf
14) K. Beauchard and E. Zuazua. Large time asymptotics for partially dissipative hyperbolic systems, Arch. Rational Mech. Anal. 199 (2011) pp. 177-227. pdf
13) K. Beauchard. Local controllability and non controllability of a 1D wave equation, Journal of Differential Equations, 250 (2011) p. 2064-2098. pdf
12) K. Beauchard and V. Nersesyan. Semi-global weak stabilization of bilinear Schrödinger equations, CRAS, Volume 348, Issues 19-20, October 2010, p. 1073-1078. pdf
11) K. Beauchard and C. Laurent, Local controllability of linear and nonlinear Schrödinger equations with bilinear control, J. Math. Pures et Appl., Volume 94, Issue 5, November 2010, Pages 520-554. pdf
10) K. Beauchard, J.-M. Coron and P. Rouchon. Controllability issues for continuous-spectrum systems and ensemble controllability of Bloch equations, Communications in Mathematical Physics, volume 296, Number 2, June 2010, p.525-557. pdf
9) K. Beauchard, Y. Chitour, D. Kateb and R. Long. Spectral controllability for 2D and 3D linear Schrödinger equations, J. of Functional Analysis, vol. 256, pp. 3916-3976, june, 2009. pdf
8) K. Beauchard and E. Zuazua. Some controllability results for the Kolmogorov equation, Ann. I. H. Poincaré-AN, 26 (2009), p. 1793-1815. pdf
7) F. Alouges and K. Beauchard. Magnetization switching on small ferromagnetic ellipsoidal samples, ESAIM:COCV, 15 (2009), p. 676-711. pdf
6) K. Beauchard and M. Mirrahimi. Practical stabilization of a quantum particle in a one-dimensional infinite square potential well, SIAM J. Control Optim., 48 (2009), no. 2, p. 1179-1205. pdf
5) K. Beauchard. Local controllability of a 1D beam equation, SIAM J. Control Optim., Volume 47, Issue 3, pp. 1219-1273 (2008). pdf
4) K. Beauchard. Controllability of a quantum particule in a 1D variable domain, ESAIM:COCV, volume 14, number 1, (2008) p. 105-147. pdf
3) K. Beauchard, J.-M. Coron, M. Mirrahimi, P. Rouchon. Implicit Lyapunov control of finite dimensional Schrödinger equations, Systems and Control Letters, 56: 388-395, May 2007. pdf
2) K. Beauchard, J.-M. Coron. Controllability of a quantum particle in a moving potential well, J. of Functional Analysis, 232 (2006) p. 328-389. pdf
1) K. Beauchard. Local controllability of a 1D Schrödinger equation, J. Math. Pures et Appl., 84:851-956, July 2005. pdf

Soutien partiel de l'ANR Projet Blanc BLAN-3-139579. (CQUID) puis ANR Projet Blanc EMAQS ANR-2011-BS01-017-01.

PROCEEDINGS ET AUTRES TEXTES :


7) K. Beauchard and P. Cannarsa. Inverse coefficient problem for Grushin-type parabolic operators. Procedding of the conference 'ODEs, Inverse problems and Control' [Cortona, Italie] ( arXiv:1312.2184) pdf
6) K. Beauchard, J.-M. Coron and P. Rouchon. Garder le contrôle... à l'aide des mathématiques. Brochure 'explosion des mathématiques' de la SMAI, 2013
5) K. Beauchard and P. Rouchon. Bilinear control of Schrödinger PDEs. Encyclopedia of Systems and Control, edited by Tariq Samad and John Baillieul, to appear, 2013 (tutorial article) pdf
4) K. Beauchard. Null controllability of degenerate parabolic equations of Grushin and Kolmogorov type. Texte du séminaire Laurent Schwarz (mars 2012) pdf
3) K. Beauchard, N. Zarrouati-Vissière and P. Rouchon. Rotational and translational bias estimation based on depth and image measurements. Procedding for CDC 2012.
2) S. Dudret, K. Beauchard, F. Ammouri, P. Rouchon. Stability and asymptotic observers of binary distillation processes described by nonlinear convection/diffusion models. American Control Conference, pp:3352-3358, 2012 pdf
1) F. Alouges, K. Beauchard, M. Sigalotti. Magnetization switching in small ferromagnetic ellipsoidal samples, Proceddings for the 48th IEEE Conference on Decision and Control and the 28th Chinese Control Conference, in Shanghai, 2009. pdf

HDR :

- Analyse et contrôle de quelques EDP, soutenue le 9 novembre 2010, à l'ENS Cachan, Jury: Nicolas Burq (Rapporteur), Piermarco Cannarsa (Rapporteur), Jean-Michel Coron, Andrei Fursikov, Jean-Pierre Puel (Rapporteur), Pierre Rouchon, Enrique Zuazua. pdf

THESE :

- Contribution à l'étude de la contrôlabilité et de la stabilisation de l'équation de Schrödinger, soutenue en décembre 2005, à l'Université d'Orsay, Jury: Jean-Pierre Puel (Président du jury), Jean-Michel Coron (directeur de thèse), Jean-Pierre Raymond, Pierre Rouchon, Gabriel Turinici. Rapporteurs: Gilles Lebeau, Enrique Zuazua. pdf

DOCTORANTS :

- sept 2010- dec 2013: Morgan Morancey
- sept 2013- : Ivan Moyano

ACTIVITE EDITORIALE :

- Associate editor pour ESAIM:COCV et Mathematical control and related fields