Nabile Boussaïd

Thèse & Habilitation

[Bou06a]

N. Boussaid. « Étude de la stabilité des petites solutions stationnaires pour une classe déquations de Dirac non linéaires ». Thèse de Doctorat. Université Paris-Dauphine, juill. 2006. url : http://tel.archives-ouvertes.fr/tel-00108459.

[Bou14]

N. Boussaid. « Non linear models from relativistic quantum mechanics : spectral and asymptotic analysis and related problems ». Habilitation à diriger des recherches. Université de Franche-Comté, nov. 2014. url : https://tel.archives-ouvertes.fr/tel-01094575.

Livre & Chapitre

[BC19b]

N. Boussaid et A. Comech. « Nonlinear Dirac equation ». T. 244. Mathematical Surveys and Monographs. Spectral stability of solitary waves. American Mathematical Society, Providence, RI, [2019] ©2019, p. vi+297. isbn : 978-1-4704-4395-5.

[Cue+18]

J. Cuevas-Maraver, N. Boussaid, A. Comech, R. Lan, P. G. Kevrekidis et A. Saxena. « Solitary waves in the nonlinear Dirac equation ». In : Nonlinear Systems. Vol. 1. Underst. Complex Syst. Springer, Cham, 2018, p. 89-143. isbn : 978-3-319-66765-2; 978-3-319-66766-9.

Publications

[Bou06b]

N. Boussaid. Stable directions for small nonlinear Dirac standing waves. In : Comm. Math. Phys. 268.(3) (2006), p. 757-817. issn : 0010-3616. doi : 10.1007/s00220-006-0112-3.

[Bou08]

N. Boussaid. On the asymptotic stability of small nonlinear Dirac standing waves in a resonant case. In : SIAM J. Math. Anal. 40.(4) (2008), p. 1621-1670. issn : 0036-1410. doi : 10.1137/ 070684641.

[BB10]

L. Boulton et N. Boussaid. Non-variational computation of the eigenstates of Dirac operators with radially symmetric potentials. In : LMS J. Comput. Math. 13 (2010), p. 10-32. issn : 1461-1570. doi : 10.1112/S1461157008000429. Code added to T. Betcke, N. J. Higham, V. Mehrmann, C. Schröder et F. Tisseur. NLEVP: A Collection of Nonlinear Eigenvalue Problems. Fév. 2013. doi : 10.1145/2427023.2427024. url : http://www.mims.manchester.ac.uk/research/numerical-analysis/nlevp.html.

[BG10]

N. Boussaid et S. Golénia. Limiting absorption principle for some long range perturbations of Dirac systems at threshold energies. In : Comm. Math. Phys. 299.(3) (2010), p. 677-708. issn : 0010-3616. doi : 10.1007/s00220-010-1099-3.

[BDF11]

N. Boussaid, P. D’Ancona et L. Fanelli. Virial identity and weak dispersion for the magnetic Dirac equation. In : J. Math. Pures Appl. (9) 95.(2) (2011), p. 137-150. issn : 0021-7824. doi : 10.1016/j.matpur.2010.10.004.

[BBL12]

L. Boulton, N. Boussaid et M. Lewin. Generalised Weyl theorems and spectral pollution in the Galerkin method. In : J. Spectr. Theory 2.(4) (2012), p. 329-354. issn : 1664-039X. doi : 10.4171/JST/32.

[BC12]

N. Boussaid et S. Cuccagna. On stability of standing waves of nonlinear Dirac equations. In : Comm. Partial Differential Equations 37.(6) (2012), p. 1001-1056. issn : 0360-5302. doi : 10.1080/03605302.2012.665973.

[BCC13c]

N. Boussaid, M. Caponigro et T. Chambrion. Weakly coupled systems in quantum control. In : IEEE Trans. Automat. Control 58.(9) (2013), p. 2205-2216. issn : 0018-9286. doi : 10.1109/ TAC.2013.2255948.

[BBB14]

G. R. Barrenechea, L. Boulton et N. Boussaid. Finite Element Eigenvalue Enclosures for the Maxwell Operator. In : SIAM Journal on Scientific Computing 36.(6) (2014), A2887-A2906. doi : 10.1137/140957810. eprint : http://dx.doi.org/10.1137/140957810.

[BBB16]

G. R. Barrenechea, L. Boulton et N. Boussaid. Local two-sided bounds for eigenvalues of self-adjoint operators. In : Numerische Mathematik (2016), 1??34. issn : 0945-3245. doi : 10.1007/s00211-016-0822-1.

[BC16]

N. Boussaid et A. Comech. On spectral stability of the nonlinear Dirac equation. In : J. Funct. Anal. 271.(6) (2016), p. 1462-1524. issn : 0022-1236. doi : 10.1016/j.jfa.2016.04.013.

[Bel+17]

J. Bellazzini, N. Boussaid, L. Jeanjean et N. Visciglia. Existence and stability of standing waves for supercritical NLS with a partial confinement. In : Comm. Math. Phys. 353.(1) (2017), p. 229-251. issn : 0010-3616. doi : 10.1007/s00220-017-2866-1.

[BC17]

N. Boussaid et A. Comech. Nonrelativistic asymptotics of solitary waves in the Dirac equation with Soler-type nonlinearity. In : SIAM J. Math. Anal. 49.(4) (2017), p. 2527-2572. issn : 0036-1410. doi : 10.1137/16M1081385.

[BC18]

N. Boussaid et A. Comech. Spectral stability of bi-frequency solitary waves in Soler and Dirac-Klein-Gordon models. In : Commun. Pure Appl. Anal. 17.(4) (2018), p. 1331-1347. issn : 1534-0392. doi : 10.3934/cpaa.2018065.

[BC19a]

N. Boussaid et A. Comech. Spectral stability of small amplitude solitary waves of the Dirac equation with the Soler-type nonlinearity. In : J. Funct. Anal. 277.(12) (2019), p. 108289. issn : 0022-1236. doi : 10.1016/j.jfa.2019.108289.

[BCC20]

N. Boussaid, M. Caponigro et T. Chambrion. Regular propagators of bilinear quantum systems. In : J. Funct. Anal. 278.(6) (2020), p. 108412. issn : 0022-1236. doi : 10.1016/j.jfa. 2019.108412.

[BC21]

N. Boussaid et A. Comech. Limiting absorption principle and virtual levels of operators in Banach spaces. In : Annales mathématiques du Québec (2021). issn : 2195-4763. doi : 10.1007/s40316-021-00181-7.

[Bou+23]

N. Boussaid, C. Cacciapuoti, R. Carlone, A. Comech, D. Noja et A. Posilicano. Spectral stability and instability of solitary waves of the Dirac equation with concentrated nonlinearity. In : Commun. Pure Appl. Anal. 22.(10) (2023), p. 3029-3067. issn : 1534-0392,1553-5258. doi : 10.3934/cpaa.2023098.

[CBC23]

T. Chambrion, N. Boussaid et M. Caponigro. On the controllability in projections for linear quantum systems. In : to appear in “Analysis and Numerics of Design, Control and Inverse Problems” (G. Floridia & E. Zuazua Eds), Springer INdAM Series, Springer Singapore (avr. 2023).

[BBD24]

J. Borthwick, N. Boussaid et T. Daudé. Inverse Regge poles problem on a warped ball. In : Inverse Probl. Imaging 18.(1) (2024), p. 239-270. issn : 1930-8337,1930-8345. doi : 10.3934/ ipi.2023031.

[BCC24]

N. Boussaid, M. Caponigro et T. Chambrion. Switching Controls for Conservative Bilinear Quantum Systems with Discrete Spectrum. In : To appear in SIAM J. on Control and Optimization (2024).

Actes de conférences avec comité de lecture

[BCC12a]

N. Boussaid, M. Caponigro et T. Chambrion. « Approximate controllability of the Schrödinger equation with a polarizability term ». In : Decision and Control (CDC), 2012 IEEE 51st Annual Conference on. IEEE. 2012, p. 3024-3029. doi : 10.1109/CDC.2012.6426619.

[BCC12b]

N. Boussaid, M. Caponigro et T. Chambrion. « Implementation of logical gates on infinite dimensional quantum oscillators ». In : 2012 American Control Conference (ACC). Juin 2012, p. 5825-5830. doi : 10.1109/ACC.2012.6315502.

[BCC12c]

N. Boussaid, M. Caponigro et T. Chambrion. « Periodic control laws for bilinear quantum systems with discrete spectrum ». In : 2012 American Control Conference (ACC). Juin 2012, p. 5819-5824. doi : 10.1109/ACC.2012.6315436.

[BCC12d]

N. Boussaid, M. Caponigro et T. Chambrion. « Small time reachable set of bilinear quantum systems ». In : Decision and Control (CDC), 2012 IEEE 51st Annual Conference on. IEEE. 2012, p. 1083-1087. doi : 10.1109/CDC.2012.6426208.

[BCC12e]

N. Boussaid, M. Caponigro et T. Chambrion. « Which notion of energy for bilinear quantum systems? » In : Proceedings of the 4th IFAC Workshop on Lagrangian and Hamiltonian Methods for Non Linear Control, pp 226-230, 29-31 août 2012. 2012, p. 226-230. doi : 10.3182/ 20120829-3-IT-4022.00034.

[BCC13a]

N. Boussaid, M. Caponigro et T. Chambrion. « Energy Estimates for Low Regularity Bilinear Schrödinger Equations ». In : Control of Systems Governed by Partial Differential Equations. T. 1. 1. 2013, p. 25-30. doi : 10.3182/20130925-3-FR-4043.00046.

[BCC13b]

N. Boussaid, M. Caponigro et T. Chambrion. « Total variation of the control and energy of bilinear quantum systems ». In : Decision and Control (CDC), 2013 IEEE 52nd Annual Conference on. Déc. 2013, p. 3714-3719. doi : 10.1109/CDC.2013.6760455.

[BCC14b]

N. Boussaid, M. Caponigro et T. Chambrion. « Efficient finite dimensional approximations for the bilinear Schrodinger equation with bounded variation controls ». In : Proceedings of the 21st International Symposium on Mathematical Theory of Networks and Systems (MTNS2014). Groningen, Netherlands, juill. 2014, p. 1889-1891. isbn : 9789036763219; 9036763215. arXiv : 1406.2260 [math.AP].

[BCC15]

N. Boussaid, M. Caponigro et T. Chambrion. « An approximate controllability result with continuous spectrum : the Morse potential with dipolar interaction ». In : SIAM Conference on Control and its applications. Paris, France, juill. 2015. isbn : 9781510811539.

[BCC19a]

N. Boussaid, M. Caponigro et T. Chambrion. « Impulsive control of the bilinear Schrödinger equation: propagators and attainable sets ». In : 2019 IEEE 58th Conference on Decision and Control (CDC). Déc. 2019, p. 2316-2321. doi : 10.1109/CDC40024.2019.9029277.

[BCC19b]

N. Boussaid, M. Caponigro et T. Chambrion. « On the Ball-Marsden-Slemrod obstruction for bilinear control systems ». In : 2019 IEEE 58th Conference on Decision and Control (CDC). Déc. 2019, p. 4971-4976. doi : 10.1109/CDC40024.2019.9029511.

[BCC]

N. Boussaïd, M. Caponigro et T. Chambrion. « Controllability of quantum systems with relatively bounded control potentials^* ». In : 2023 Proceedings of the Conference on Control and its Applications (CT), p. 141-148. doi : 10.1137/1.9781611977745.19. eprint : https://epubs.siam.org/doi/pdf/10.1137/1.9781611977745.19.

Prépublications

[Bou07]

N. Boussaid. A stability result for small stationary solutions of a class of nonlinear Dirac equations. 2007. url : http://basepub.dauphine.fr/xmlui/handle/123456789/6543.

[BCC14a]

N. Boussaid, M. Caponigro et T. Chambrion. Approximate controllability of the Schrödinger Equation with a polarizability term in higher Sobolev norms. Juin 2014. arXiv : 1406.3846 [math.AP].

[BFJ19]

N. Boussaid, A. J. Fernández et L. Jeanjean. Some remarks on a minimization problem associated to a fourth order nonlinear Scrhödinger equation. Oct. 2019. arXiv : 1910.13177 [math.AP].

[BC24]

N. Boussaid et A. Comech. Virtual levels and virtual states of linear operators in Banach spaces. Applications to Schroedinger operators. 2024. arXiv : 2101.11979 [math.AP].