Alessandro Duca




Centre Inria Nancy - Grand Est (France).


IECL : Institut Elie Cartan de Lorraine (Nancy, France).





Scientific interests

• During my Ph.D. thesis, I studied the controllability of the bilinear Schrödinger equation on intervals in [7,9] and on compact graphs in [6,8]. Afterwards, I addressed the problem on infinite networks in [2,3] in collaboration with Kaïs Ammari.

• I'm studying the controllability of the non-linear Schrödinger equation via bilinear controls in collaboration with Vahagn Nersesyan. In [13], we proved the approximate controllability between eigenmodes on a torus of arbitrary dimension in any positive time. In [14], we proved the local exact controllability on bounded intervals equipped of Dirichlet type boundary conditions.

• I am collaborating with Piermarco Cannarsa and Cristina Urbani to study the exact controllability of parabolic equations on networks via bilinear controls. Our first work on the subject is [4].

• I studied in [12] the controllability of a 1D Schrödinger equation via quasi-adiabatic controls with Dmitry Turaev and Romain Joly. I seek for numerical evidences for such result in collaboration with Carlos Castro in [5].

• I addressed with Romain Joly in [10] the well-posedness of the Schrödinger equation on time-varying domains. In collaboration with Dmitry Turaev, we study the controllability of quantum systems via quasi-adiabatic deformations of domains in [11].

• With Mama Abdelli and Akram Ben Aissa, I studied the well-posedness and the exponential stability of a Euler-Bernoulli beam conveying fluid equations in [1].

Positions held:

Grants and Projects:


  1. M. Abdelli, A. Ben Aissa, A. Duca, Well-posedness and exponential decay for the Euler-Bernoulli beam conveying fluid with non-constant velocity and dynamical boundary conditions. Zeitschrift fuer Angewandte Mathematik und Physik, 2021. DOI, arXiv.

  2. K. Ammari, A. Duca. Controllability of localized quantum states on infinite graphs through bilinear control fields. International Journal of Control, 2021. DOI, arXiv.

  3. K. Ammari, A. Duca. Controllability of periodic bilinear quantum systems on infinite graphs. Journal of Mathematical Physics, 2020.DOI, arXiv.

  4. P. Cannarsa, A. Duca, C. Urbani. Exact controllability to eigensolutions of the bilinear heat equation on compact networks. Discrete Contin. Dyn. Syst. - S, 2022. DOI, arXiv.

  5. C. Castro, A. Duca. Achieving energy permutation of modes in the Schrödinger equation with moving Dirac potentials. Mathematical Control and Related Fields, 2023, in press. HAL.

  6. A. Duca. Bilinear quantum systems on compact graphs: well-posedness and global exact controllability. Automatica J. IFAC, 2021. DOI, arXiv.

  7. A. Duca. Controllability of bilinear quantum systems in explicit times via explicit control fields. International Journal of Control, 2021. DOI, arXiv.

  8. A. Duca. Global exact controllability of bilinear quantum systems on compact graphs and energetic controllability. SIAM Journal on Control and Optimization, 2020. DOI, arXiv.

  9. A. Duca. Simultaneous global exact controllability in projection of infinite 1D bilinear Schrödinger equations. Dynamics of Partial Differential Equations, 2020. DOI, arXiv.

  10. A. Duca, R. Joly. Schrödinger equation in moving domains. Annales Henri Poincaré, 2021. DOI, arXiv.

  11. A. Duca, R. Joly, D. Turaev. Control of the Schrödinger equation by slow deformations of the domain. Annales de l'Institut Henri Poincaré, Analyse non linéaire, 2023, in press. HAL.

  12. A. Duca, R. Joly, D. Turaev. Permuting quantum eigenmodes by a quasi-adiabatic motion of the potential wall. Journal of Mathematical Physics, 2020. DOI, arXiv.

  13. A. Duca, V. Nersesyan. Bilinear control and growth of Sobolev norms for the nonlinear Schrödinger equation. Journal of the European Mathematical Society, 2023, in press. arXiv.


  1. A. Duca, V. Nersesyan. Local exact controllability of the 1D nonlinear Schrödinger equation in the case of Dirichlet boundary conditions, 2022. arXiv.

Invited speaker to talks in conferences, workshops and schools:

  1. Winter School on Control, stability and Singularities formation in Nonlinear PDE's, December 2022, Hammamet (Tunisia).

  2. Analysis and Control of (bi)linear PDEs, September 2022, Tor Vergata University of Rome (Italy).

  3. Analysis, Control and Inverse Problems for Diffusive Systems with Application to Natural and Social Sciences, July 2022, University of Bari (Italy).

  4. Journées Jeunes EDPistes, March 2022, Institut Camille Jordan, Lyon (France).

  5. Controllability of PDEs in physics models and applied sciences, February 2020, Rome (Italy).

  6. VIII Partial differential equations, optimal design and numerics, August 2019, Benasque (Spain).

  7. Identification and Control: Some challenges, June 2019, Monastir (Tunisia).

  8. GDR Dynqua Bordeaux, February 2019, Bordeaux (France).

  9. Workshop on PDE's: Modelling & Theory, 2018, Monastir (Tunisia).

  10. Journées Jeunes EDPistes, March 2018, Nancy (France), poster exposition.

  11. Second School and Workshop: Mathematical Challenges in Quantum Mechanics, February 2018, Rome (Italy).

  12. Colloque INFINITI IHP, November 2017, Paris (France), poster exposition.

  13. EDP-Normandie, October 2017, Caen (France), poster exposition.

  14. Mathematical Control Theory, June 2017, Porquerolles (France).

  15. La journée DISQUO, December 2016, Inria Paris (France).

  16. Réunion du GT EDP May 2016, l'école des Mines à Paris (France).

Invited speaker to seminars:

  1. March 2023 (control group workshop), Institut Élie Cartan de Lorraine, Nancy (France).

  2. February 2023 (control group workshop), Institut Élie Cartan de Lorraine, Nancy (France).

  3. January 2023 (control group workshop), Institut Élie Cartan de Lorraine, Nancy (France).

  4. January 2023, INRIA, Nancy (France).

  5. April 2022, University of Hagen (Germany).

  6. December 2021, research group ``Mathematics in Cairo'' (Egypt).

  7. Novembre 2021, Institut Élie Cartan de Lorraine, Nancy (France).

  8. October 2021, Laboratoire de Mathématiques de Toulouse (France).

  9. Avril 2021, Laboratoire de Mathématiques de Versailles (France).

  10. Avril 2021, Laboratoire de Mathématiques et leurs Applications de Valenciennes (France).

  11. March 2021, Gran Sasso Science Institute (Italy).

  12. January 2020, University of Monastir (Tunisia).

  13. December 2019, Laboratoire de Mathématiques de Toulouse (France).

  14. December 2019 (control group workshop), Laboratoire de Mathématiques de Toulouse (France).

  15. May 2019, Université Savoie Mont Blanc, Chambery (France).

  16. January 2019, University of Monastir (Tunisia).

  17. December 2017, Institut Fourier of Grenoble (France).

  18. November 2017, Institut Élie Cartan de Lorraine, Nancy (France).