Home | Publications |
---|

**Articles:**

- Perfectly matched layers in 1-d: Energy decay for continuous and semi-discrete waves, with Enrique Zuazua. Numerische Mathematik, 2008, 109(4), pages 597-634. The original publication is available at http://www.spingerlink.com/.
- On the observability of time-discrete conservative linear systems, with Chuang Zheng and Enrique Zuazua. Final version in Journal of Functional Analysis, 2008, 254(12), pages 3037-3078, DOI: 10.1016/j.jfa.2008.03.005.
- Control and stabilization properties for a singular heat equation with an inverse square potential. Final version in Communications in PDE, 2008, 33(11), pages 1996-2019, DOI:10.1080/03605300802402633.
- Uniformly exponentially stable approximations for a class of damped systems, with Enrique Zuazua, final version in Journal de Mathématiques Pures et Appliquées, 2009, 91(1), pages 20-48, DOI:10.1016/j.matpur.2008.09.002.
- Approximate controllability for a system of Schrödinger equations modeling a single trapped ion, with Jean-Pierre Puel, Final version in Annales de l'Institut Henri Poincaré : Analyse non linéaire, 26 (2009), no. 6, 2111--2136.
- Spectral conditions for admissibility and observability of wave systems: Applications to finite element schemes, Numerische Mathematik, 2009, 113(3), pages 377-415. The original publication is available at http://www.spingerlink.com/.
- Uniform observability estimates for the 1-D discretized wave equation and the random choice method, with Jean-Michel Coron et Olivier Glass, Comptes rendus de l'Académie des Sciences : Mathématiques, 2009, 347(9-10), pages 505--510, original publication.
- Observability properties of a semi-discrete 1D wave equation derived from a mixed finite element method on nonuniform meshes, final version ESAIM Control Optim. Calc. Var. 16 (2010), no. 2, 298--326.
- On the observability of abstract time-discrete linear conservative systems, with Julie Valein, final version in Revista Matematica Complutense, 23 (2010), no. 1, 163--190, DOI:10.1007/s13163-009-0014-y.
- A systematic method for building smooth controls for smooth data, with Enrique Zuazua, final version in Discrete Contin. Dyn. Syst. Ser. B 14 (2010), no. 4, 1375--1401.
- Spectral conditions for admissibility and observability of Schrödinger systems: Applications to finite element discretizations, final version in Asymptotic Analysis 71(2011), no.1--2, 1--32.
- Sharp observability estimates for the heat equations, with Enrique Zuazua, final version in Arch. Ration. Mech. Anal. 202 (2011), no. 3, 975--1017.
- Observability of heat processes by transmutation without geometric restrictions, with Enrique Zuazua, final version in Mathematical Control and Related Fields, 1 (2011), no 2, 177--187.
- Uniform stability estimates for the discrete Calderon problems, with Frédéric de Gournay, final version in Inverse Problems 27 (2011)--125012.
- Local exact controllability for the one-dimensional compressible Navier-Stokes equation, with Olivier Glass, Sergio Guerrero and Jean-Pierre Puel, final version in Arch. Ration. Mech. and Anal., 206 (2012), no.1, 189--238.
- Convergence of an inverse problem for a 1-D discrete wave equation, with Lucie Baudouin, final version in SIAM Cont. and Opt., 51 (2013) no. 1, 556--598.
- Global Carleman estimates for waves and applications, with Lucie Baudouin and Maya de Buhan, final version in Comm. in PDE, 38:5 (2013), 823--859.
- Long-time behavior for the two-dimensional motion of a disk in a viscous fluid, with Matthieu Hillairet and Christophe Lacave, final version in Comm. Math. Phys. 329 (2014), no. 1, 325--382.
- Controllability of a simplified model of fluid-structure interaction, with M. Vanninathan, final version in ESAIM COCV, 20(2), 2014, pp 547--575.
- Dependence of high-frequency waves with respect to potentials, with Belhassen Dehman, final version in SIAM Journal of Control and Optimization 52 (2014), no.6 373--750.
- Transmutation techniques and observability for time-discrete approximation schemes of conservative systems, with Enrique Zuazua, final version in Numer. Math. 130 (2015), no. 3, 425--466.
- Stability of an inverse problem for the discrete wave equation and convergence results, with Lucie Baudouin and Axel Osses, final version in Journal de Mathématiques Pures et Appliquées (9) 103 (2015), no. 6, 1475--1522.
- Local controllability to trajectories for non-homogeneous incompressible Navier-Stokes equations, with Mehdi Badra and Sergio Guerrero, final version in Annales de l'Institut Henri Poincaré: Analyse non linéaire 33 (2016), no. 2, 529--574.
- Numerical meshes ensuring uniform observability of 1d waves: construction and analysis, with Aurora Marica and Enrique Zuazua, final version in IMA Journal of Numerical Analysis 36 (2016), no. 2, 503--542. .
- Local exact controllability for the 2 and 3-d compressible Navier-Stokes equations, with Olivier Glass and Sergio Guerrero, final version in Comm. Partial Differential Equations 41 (2016), no. 11, 1660--1691.
- Local boundary controllability to trajectories for the 1d compressible Navier Stokes equations, with Marc Savel, final version in ESAIM Control Optim. Calc. Var. 24 (2018), no.1 , 211--235.
- Dissipative boundary conditions for 2x2 hyperbolic systems of conservation laws for entropy solutions in BV, with Jean-Michel Coron, Shyam Ghoshal, Olivier Glass and Vincent Perrollaz, final version in J. Differential Equations 262 (2017), no. 1, 1--30.
- Observability Estimates for the Wave Equation with Rough Coefficients, with Belhassen Dehman, final version in C. R. Math. Acad. Sci. Paris 355 (2017), no. 5, 499--514.
- Convergent algorithm based on Carleman estimates for the recovery of a potential in the wave equation, with Lucie Baudouin and Maya de Buhan, final version in SIAM J. Numer. Anal. 55 (2017), no. 4, 1578--1613.
- On the reachable set for the one-dimensional heat equation, with Jérémi Dardé, final version in SIAM J. Control Optim. 56 (2018), no. 3, 1692--1715.
- On the cost of observability in small times for the one-dimensional heat equation, with Jérémi Dardé, final version in Analysis and PDE, vol. 12 n. 6, 2019, 1455--1488.
- Open loop stabilization of incompressible Navier-Stokes equations in a 2d channel using power series expansion, with Shirshendu Chowdhury, complementary Maxima file, final version in Journal de Mathématiques Pures et Appliquées, Vol.130 Oct.2019, p.301--346.
- Minimal time issues for the observability of Grushin-type equations, with Karine Beauchard and Jérémi Dardé, final version in Ann. Inst. Fourier (Grenoble) 70 (2020), no. 1, 247--312.
- A conservation law with spatially localized sublinear damping, with Christophe Besse and Rémi Carles, final version in Ann. Inst. H. Poincaré Anal. Non Linéaire 37 (2020), no. 1, 13--50.
- Backward uniqueness results for some parabolic equations in an infinite rod, with Jérémi Dardé, final version in Math. Control Relat. Fields 9 (2019), no. 4, 673--696.
- Control issues and linear projection constraints on the control and on the controlled trajectory, final version in North-West. Eur. J. Math. 6 (2020), 165--198.
- Carleman based reconstruction algorithm for the waves, with Lucie Baudouin, Maya de Buhan, and Axel Osses, to appear in SIAM J. Numerical Analysis.

**Preprints:**

- Large time behaviour for the motion of a solid in a viscous incompressible fluid, with Debayan Maity, and Marius Tucsnak, submitted.
- Switching controls for analytic semigroups and applications to parabolic systems, with Felipe Wallison Chaves-Silva, Diego Araujo de Souza, submitted.
- Uniform null controllability for a parabolic equations with discontinuous diffusion coefficient, with Jérémi Dardé and Roberto Morales, submitted.
- Insensitizing controls for the heat equation with respect to boundary variations, with Pierre Lissy and Yannick Privat, submitted.

**Book:**

- Numerical Approximation of Exact Controls for Waves, with Enrique Zuazua, Springer, Springer Briefs in Mathematics (New York) 2013, Doi:10.1007/978-1-4614-5808-1

**Proceedings of conference (without Peer-review):**

- Uniform exponential decay for viscous damped systems, with Enrique Zuazua, Advances in phase space analysis of partial differential equations, 95--112, Progr. Nonlinear Differential Equations Appl., 78, Birkhauser Boston, Inc., Boston, MA, 2009.
- Observability in arbitrary small time for discrete conservative linear systems, in Some Problems in Nonlinear Hyperbolic Equations, ed. Tatsien Li, Yuejun Peng and Bopeng Rao, Series in Contemporary Mathematics CAM15, p.283--309.
- Resolvent estimates in controllability theory and applications to the discrete wave equation, Journées équations aux dérivées partielles (2009), Exp. No. 2, 18 p.
- Local exact controllability for the 1d compressible Navier-Stokes equation, Actes de Séminaire X-EDP, 2012.

**Book Chapter:**

- The wave equation: Control and numerics, with Enrique Zuazua. In P.~M. Cannarsa and J.~M. Coron, editors, Control of Partial Differential Equations, Lecture Notes in Mathematics, CIME Subseries. Springer Verlag, 2011.

PhD thesis (mainly in English), defended on November 25, 2008 in Univ. de Versailles Saint-Quentin-en-Yvelines, advisor: Jean-Pierre Puel.

Mémoire d'habilitation, defended on November 25, 2014 in Univ. Paul Sabatier Toulouse 3, parrain: Jean-Pierre Raymond.

Comments and remarks are welcome at