Alessandro Duca


E-mail

alessandro.duca@uvsq.fr

 

Address

Université Paris-Saclay, UVSQ,
Laboratoire de Mathématiques de Versailles.


Office

Bâtiment Fermat, B 3302

 


Curriculum Vitae

Version: French, English.

       

Scientific interests

• During my Ph.D. thesis, I studied the controllability of the bilinear Schrödinger equation on intervals in [5,7] and on compact graphs in [4,6]. 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 [10], we proved the approximate controllability between eigenmodes for the equation on a torus of arbitrary dimension. We are currently dealing with the global exact controllability of the equation on bounded intervals.

• I am currently collaborating with Piermarco Cannarsa and Cristina Urbani to study the exact controllability of parabolic equations on networks via bilinear controls.

• I am collaborating with Kaïs Ammari and Eric Bonnetier in order to study the spectral properties and the controllability of quantum systems defined on networks combining dielectric and negative index materials.

• I studied in [9] the controllability of a 1D Schrödinger equation via quasi-adiabatic controls in collaboration with Dmitry Turaev and Romain Joly. I am seeking for numerical evidences for such result in collaboration with Carlos Castro.

• I addressed with Romain Joly in [8] the well-posedness of the Schrödinger equation on time-varying domains. In collaboration with Dmitry Turaev, we are studying the controllability of quantum systems via quasi-adiabatic deformations of domains.

• 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:

Publications:

  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. Z. Angew. Math. Phys, 72(2):49, 2021. DOI, arXiv.

  2. K. Ammari, A. Duca. Controllability of localized quantum states on infinite graphs through bilinear control fields. To appear in 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, 61(10):101507, 2020.DOI, arXiv.

  4. A. Duca. Bilinear quantum systems on compact graphs: well-posedness and global exact controllability. Automatica J. IFAC, 123:109324, 2021. DOI, arXiv.

  5. A. Duca. Controllability of bilinear quantum systems in explicit times via explicit control fields. Internat. J. Control, 94(3):724-734, 2021. DOI, arXiv.

  6. A. Duca. Global exact controllability of bilinear quantum systems on compact graphs and energetic controllability. SIAM J. Control Optim., 58(6):3092-3129, 2020. DOI, arXiv.

  7. A. Duca. Simultaneous global exact controllability in projection of infinite 1D bilinear Schrödinger equations. Dynamics of Partial Differential Equations, 17(3):275--306, 2020. DOI, arXiv.

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

  9. A. Duca, R. Joly, D. Turaev. Permuting quantum eigenmodes by a quasi-adiabatic motion of the potential wall. Journal of Mathematical Physics, 61(10):101511, 2020. DOI, arXiv.

Preprints:

  1. A. Duca, V. Nersesyan. Bilinear control and growth of Sobolev norms for the nonlinear Schrödinger equation, 2021. arXiv.

Invited speaker to talks in conferences, workshops and schools: