Alessandro Duca

Contacts


E-mail:

alessandro.duca@univ-grenoble-alpes.fr
alessandro.duca@unito.it

 

Office:

B108

 

Address:

Université Grenoble Alpes
Institut Fourier
100 Rue des Mathématiques, 38610 Gières, France

       

Scientific interests:

• During my Ph.D. thesis, I studied the controllability of the bilinear Schrödinger equation on intervals in [2,3] and on compact graphs in [6,7]. Afterwards, I addressed the problem on infinite networks in [1,5] in collaboration with Kaïs Ammari.

• 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 am studying the well-posedness and the exponential stability of different Euler-Bernoulli beam conveying fluid equations. Our first results lead to [4].

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

Curriculum Vitae:

Status:

Publications:

  1. K. Ammari, A. Duca. Controllability of localized quantum states on infinite graphs through bilinear control fields. To appear in International Journal of Control, 2019. DOI, link1, link2.

  2. A. Duca. Controllability of bilinear quantum systems in explicit times via explicit control fields. To appear in International Journal of Control, 2019. DOI, link1, link2.

  3. A. Duca. Simultaneous global exact controllability in projection of infinite 1D bilinear SchroŐądinger equations. Dynamics of Partial Differential Equations, 17(3):275--306, 2020. DOI, link1, link2.

Preprints:

  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. link1, link2.

  2. K. Ammari, A. Duca. Controllability of periodic bilinear quantum systems on infinite graphs. link1, link2.

  3. A. Duca. Bilinear quantum systems on compact graphs: well-posedness and global exact controllability. link1, link2.

  4. A. Duca. Global exact controllability of bilinear quantum systems on compact graphs and energetic controllability. link1, link2.

  5. A. Duca, R. Joly. Schrödinger equation in moving domains. link1, link2.

  6. A. Duca, R. Joly, D. Turaev. Permuting quantum eigenmodes by a quasi-adiabatic motion of the potential wall. link1, link2.

Talks in conferences, workshops and schools: