Karine Beauchard

Professeur à l' ENS Rennes.

ENS Rennes

Avenue Robert Schumann

35170 BRUZ

Courriel : Karine.Beauchard-at-ens-rennes.fr

Bureau : Bâtiment A. Sauvy (1er étage)

Téléphone : 02.99.05.93.45

CV français English

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 :

37) K. Beauchard, P. Jaming and K. Pravda-Starov Spectral inequality for Hermite functions and null controllability for hypoelliptic quadratic equa- tions from thick sets arXiv :1804.04895 pdf

36) K. Beauchard, M. Egidi and K. Pravda-Starov Geometric conditions for the null-controllability of hypoelliptic quadratic parabolic equations with moving control supports Comptes Rendus de Mathématiques, to appear, arXiv :1804.04895 pdf

35) Karine Beauchard, Armand Koenig and Kévin Le Balc’h, Null-controllability of linear parabolic-transport systems Journal de l’École polytechnique - Mathématiques, Tome 7 (2020) p. 743-802 pdf

34) K. Beauchard and F. Marbach. Unexpected quadratic behavior for the small-time local null controllability of scalar-input parabolic equations. Journal de Maths Pures et Appliquées, arxiv 1712.09790 pdf

33) K. Beauchard, J. Darde and S. Ervedoza. Minimal time issues for the observability of Grushin-type equations. Annales de l’Institut Fourier, to appear, hal-01677037v1 pdf

32) K. Beauchard and Frédéric Marbach. Quadratic obstructions to small-time local controllability for scalar-input dfferential systems. J. Differential Equations, 264(5):3704-3774, 2018, doi:10.1016/j.jde.2017.11.028 pdf

31) K. Beauchard and K. Pravda-Starov. Null-controllability of non-autonomous Ornstein-Uhlenbeck equations, preprint 2016, arXiv :1603.05367 pdf

30) K. Beauchard and K. Pravda-Starov. Null controllability of hypoelliptic quadratic equations, preprint 2016, arXiv :1603.05367 pdf

29) K. Beauchard, J.-M. Coron and H. Teismann. Minimal time for the approximate bilinear control of Schrödinger equations, preprint 2016, hal-01333537 pdf

28) K. Beauchard and C. Laurent. Local exact controllability of the 2D-Schrödinger-Poisson system, Journal de l'Ecole Polytechnique 2017 (to appear), hal-01333627. pdf

27) K. Beauchard and C. Laurent. Bilinear control of high frequencies for a 1D Schrödinger equation, Mathematics of Control Signals and Systems 2017 (to appear), hal-01333625 pdf

26) K. Beauchard and P. Cannarsa. Heat equation on the Heisenberg group : observability and applications, Journal of Differential Equations 2017 (to appear) pdf

25) K. Beauchard, L. Miller and M. Morancey. 2D Grushin-type equations: minimal time and null controllable data Journal of Differential Equations 259 (2015), pp.5813-5845 pdf

24) K. Beauchard, H. Lange and H. Teismann. Local exact controllability of a Bose-Einstein condensate in a 1D time-varying box. SIAM Journal on Control and Optimization 2015, Vol. 53, No. 5, pp. 2781-2818. (arXiv:1303.2713) pdf

23) K. Beauchard, J.-M. Coron and H. Teismann. Minimal time for the bilinear control of Schrödinger equations, Systems and Control Letters, 71, 2014, p. 1-6 pdf

22) K. Beauchard, B. Helffer, R. Henry, L. Robbiano. Degenerate parabolic operators of Kolmogorov type with a geometric control condition, ESAIM Control Optim. Calc. Var. 21 (2015), no. 2, 487--512. pdf

21) K. Beauchard, N. Zarrouati-Vissière and P. Rouchon. Rotational and translational bias estimation based on depth and image measurements. Siam J. Control Optim. Vol. 52, No. 6, pp. 3463-3495, 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, 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, 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. Automatica, vol. 49, p. 2133-2137, 2013. pdf

16) K. Beauchard, P. Cannarsa, R. Guglielmi. Null controllability of Grushin-type operators in dimension two, Journal of the European Mathematical Society, vol. 16, no. 1, p 67-101, 2014. 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