Professeur à l' ENS Rennes, membre de l'IRMAR
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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 pdf
- analyse et contrôle d'équations aux dérivées partielles
- interaction entre géométrie (crochets de Lie) et analyse dans le contrôle des équations différentielles, généralisation aux équations aux dérivées partielles
- contrôle bilinéaire, contrôle quantique : contrôlabilité exacte/approchée, stabilisation feedback des équations de Schrödinger et de Bloch
- contrôle d'équations paraboliques dégénérées de type hypoelliptique (Grushin, Heisenberg, Kolmogorov, Ornstein-Uhlenbeck,...): temps minimal et condition de contrôle géométrique
- problèmes inverses, observateurs asymptotiques
46) K. Beauchard. Quadratic terms, Lie brackets and local controllability. ICM 2026 proceeding pdf
45)K. Beauchard, R. Carles, E. Pozzoli. Small-time approximate controllability of the logarithmic Schrödinger equation. arXiv:2510.14461 pdf
44) K. Beauchard, A. Laurent, F. Marbach. Control theory and splitting methods. arXiv:2407.02127 pdf
43)K. Beauchard, F. Marbach, T. Perrin. Small-time local control of a Schrödinger equation: negative and positive quadratic results. arXiv:2501.03882 pdf
42)K. Beauchard, E. Pozzoli. Small-time approximate controllability of bilinear Schrödinger equations and diffeomorphisms. Annales de l’Institut Henri Poincaré C-Analyse Non Linéaire (2025) pdf
41)K. Beauchard, E. Pozzoli. Examples of small-time controllable Schrödinger equations. Annales Henri Poincaré, A-Theoretical Math. Phys (2025) pdf
40)K. Beauchard, F. Marbach. A unified approach of obstructions to small-time local controllability for scalar-input systems. Journal of Dynamical and Control Systems (77 pages) pdf
39)K. Beauchard, J. Le Borgne, F. Marbach. Growth of structure constants of free Lie algebras relative to Hall bases. Journal of Algebra, 612:281-378, 2022 pdf
38) K. Beauchard, J. Le Borgne, F. Marbach. On expansions for nonlinear systems, error estimates and convergence issues. Comptes Rendus. Mathématique, 361:97-189, 2023 pdf
37) K. Beauchard, P. Jaming, K. Pravda-Starov. Spectral inequality for Hermite functions and null controllability for hypoelliptic quadratic equations from thick sets. Studia Math. 260 (2021), no.1, 1-43 pdf
36) K. Beauchard, M. Egidi, K. Pravda-Starov. Geometric conditions for the null-controllability of hypoelliptic quadratic parabolic equations with moving control supports. Comptes Rendus. Mathématique, Volume 358 (2020) no. 6 p. 651-700 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, S. Ervedoza, J. Darde. Minimal time issues for the observability of Grushin-type equations. Annales de l’Institut Fourier, 70 (2020), no. 1, 247–312 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, K. Pravda-Starov. Null-controllability of non-autonomous Ornstein-Uhlenbeck equations. Journal of Mathematical Analysis and Applications, 456, no. 1, 496-524, 2017 pdf
30) K. Beauchard, K. Pravda-Starov. Null-controllability of hypoelliptic quadratic differential equations. Journal de l’École Polytechnique, Math. 5, p.1-43, 2018 pdf
29) K. Beauchard, J.-M. Coron, H. Teismann. Minimal time for the approximate bilinear control of Schrödinger equations. Mathematical Methods in the Applied Sciences 41(4), January 2018 pdf
28) K. Beauchard, C. Laurent. Local exact controllability of the 2D-Schrödinger-Poisson system. Journal de l’École polytechnique - Mathématiques, 4, p. 287-336, 2017. pdf
27) K. Beauchard, C. Laurent. Bilinear control of high frequencies for a 1D Schrödinger equation. Mathematics of Control Signals and Systems, Volume 17, Issue 2, June 2017 pdf
26) K. Beauchard, P. Cannarsa. Heat equation on the Heisenberg group: observability and applications. Journal of Differential Equations, Volume 262, Issue 8, p. 4475-4521, April 2017 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
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, 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
- 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
- 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