Team, Visitors, External Collaborators
Overall Objectives
Research Program
Application Domains
Highlights of the Year
New Software and Platforms
New Results
Bilateral Contracts and Grants with Industry
Partnerships and Cooperations
Dissemination
Bibliography
XML PDF e-pub
PDF e-Pub


Bibliography

Major publications by the team in recent years
[1]
X. Antoine, Q. Tang, J. Zhang.
On the numerical solution and dynamical laws of nonlinear fractional Schrödinger/Gross-Pitaevskii equations, in: Int. J. Comput. Math., 2018, vol. 95, no 6-7, pp. 1423–1443.
https://doi.org/10.1080/00207160.2018.1437911
[2]
N. Burq, D. Dos Santos Ferreira, K. Krupchyk.
From semiclassical Strichartz estimates to uniform Lp resolvent estimates on compact manifolds, in: Int. Math. Res. Not. IMRN, 2018, no 16, pp. 5178–5218.
https://doi.org/10.1093/imrn/rnx042
[3]
L. Bălilescu, J. San Martín, T. Takahashi.
Fluid-structure interaction system with Coulomb's law, in: SIAM Journal on Mathematical Analysis, 2017.
https://hal.archives-ouvertes.fr/hal-01386574
[4]
L. Gagnon.
Lagrangian controllability of the 1-dimensional Korteweg–de Vries equation, in: SIAM J. Control Optim., 2016, vol. 54, no 6, pp. 3152–3173.
https://doi.org/10.1137/140964783
[5]
O. Glass, A. Munnier, F. Sueur.
Point vortex dynamics as zero-radius limit of the motion of a rigid body in an irrotational fluid, in: Inventiones Mathematicae, 2018, vol. 214, no 1, pp. 171-287. [ DOI : 10.1007/s00222-018-0802-4 ]
https://hal.archives-ouvertes.fr/hal-00950544
[6]
C. Grandmont, M. Hillairet, J. Lequeurre.
Existence of local strong solutions to fluid-beam and fluid-rod interaction systems, in: Annales de l'Institut Henri Poincaré (C) Non Linear Analysis, July 2019, vol. 36, no 4, pp. 1105-1149. [ DOI : 10.1016/j.anihpc.2018.10.006 ]
https://hal.inria.fr/hal-01567661
[7]
A. Munnier, K. Ramdani.
Calderón cavities inverse problem as a shape-from-moments problem, in: Quarterly of Applied Mathematics, 2018, vol. 76, pp. 407-435, forthcoming.
https://hal.inria.fr/hal-01503425
[8]
K. Ramdani, J. Valein, J.-C. Vivalda.
Adaptive observer for age-structured population with spatial diffusion, in: North-Western European Journal of Mathematics, 2018, vol. 4, pp. 39-58, forthcoming.
https://hal.inria.fr/hal-01469488
[9]
J.-F. Scheid, J. Sokolowski.
Shape optimization for a fluid-elasticity system, in: Pure Appl. Funct. Anal., 2018, vol. 3, no 1, pp. 193–217.
Publications of the year

Articles in International Peer-Reviewed Journals

[10]
X. Antoine, L. Emmanuel.
Explicit computation of Robin parameters in optimized Schwarz waveform relaxation methods for Schrödinger equations based on pseudodifferential operators, in: Communications in Computational Physics, 2019, forthcoming. [ DOI : 10.4208/cicp.OA-2018-0259 ]
https://hal.archives-ouvertes.fr/hal-01929066
[11]
X. Antoine, L. Emmanuel.
On the rate of convergence of Schwarz waveform relaxation methods for the time-dependent Schrödinger equation, in: Journal of Computational and Applied Mathematics, 2019, vol. 354, pp. 15-30. [ DOI : 10.1016/j.cam.2018.12.006 ]
https://hal.archives-ouvertes.fr/hal-01649736
[12]
X. Antoine, E. Lorin.
A simple pseudospectral method for the computation of the time-dependent Dirac equation with Perfectly Matched Layers, in: Journal of Computational Physics, 2019, vol. 395, pp. 583-601. [ DOI : 10.1016/j.jcp.2019.06.020 ]
https://hal.archives-ouvertes.fr/hal-02340843
[13]
X. Antoine, E. Lorin.
Asymptotic convergence rates of SWR methods for Schrödinger equations with an arbitrary number of subdomains, in: Multiscale Science and Engineering, 2019, vol. 1, no 1, pp. 34-46. [ DOI : 10.1007/s42493-018-00012-y ]
https://hal.archives-ouvertes.fr/hal-02340909
[14]
X. Antoine, E. Lorin.
Towards perfectly matched layers for time-dependent space fractional PDEs, in: Journal of Computational Physics, 2019, vol. 391, pp. 59-90. [ DOI : 10.1016/j.jcp.2019.04.025 ]
https://hal.archives-ouvertes.fr/hal-01962622
[15]
E. Augeraud-Véron, C. Choquet, E. Comte.
Optimal buffer zone for the control of groundwater pollution from agricultural activities, in: Applied Mathematics and Optimization, 2019, to appear, forthcoming. [ DOI : 10.1007/s00245-019-09638-2 ]
https://hal.inria.fr/hal-02380678
[16]
M. Badra, T. Takahashi.
Gevrey regularity for a system coupling the Navier-Stokes system with a beam equation, in: SIAM Journal on Mathematical Analysis, 2019, forthcoming.
https://hal.archives-ouvertes.fr/hal-02160011
[17]
L. Baudouin, E. Crépeau, J. Valein.
Two approaches for the stabilization of nonlinear KdV equation with boundary time-delay feedback, in: IEEE Transactions on Automatic Control, April 2019, vol. 64, no 4, pp. 1403-1414, https://arxiv.org/abs/1711.09696. [ DOI : 10.1109/TAC.2018.2849564 ]
https://hal.laas.fr/hal-01643321
[18]
M. Boulakia, S. Guerrero, T. Takahashi.
Well-posedness for the coupling between a viscous incompressible fluid and an elastic structure, in: Nonlinearity, 2019, vol. 32, pp. 3548-3592. [ DOI : 10.1088/1361-6544/ab128c ]
https://hal.inria.fr/hal-01939464
[19]
N. Boussaid, M. Caponigro, T. Chambrion.
Regular propagators of bilinear quantum systems, in: Journal of Functional Analysis, 2019, https://arxiv.org/abs/1406.7847, forthcoming. [ DOI : 10.1016/j.jfa.2019.108412 ]
https://hal.archives-ouvertes.fr/hal-01016299
[20]
T. Chambrion, L. Thomann.
A topological obstruction to the controllability of nonlinear wave equations with bilinear control term, in: SIAM Journal on Control and Optimization, 2019, vol. 57, no 4, pp. 2315-2327, https://arxiv.org/abs/1809.07107. [ DOI : 10.1137/18M1215207 ]
https://hal.archives-ouvertes.fr/hal-01876952
[21]
T. Chambrion, L. Thomann.
On the bilinear control of the Gross-Pitaevskii equation, in: Annales de l'Institut Henri Poincaré (C) Non Linear Analysis, 2020, https://arxiv.org/abs/1810.09792, forthcoming.
https://hal.archives-ouvertes.fr/hal-01901819
[22]
I. A. Djebour, T. Takahashi.
On the existence of strong solutions to a fluid structure interaction problem with Navier boundary conditions, in: Journal of Mathematical Fluid Mechanics, 2019, forthcoming. [ DOI : 10.1007/s00021-019-0440-7 ]
https://hal.archives-ouvertes.fr/hal-02061542
[23]
O. Glass, C. Lacave, A. Munnier, F. Sueur.
Dynamics of rigid bodies in a two dimensional incompressible perfect fluid, in: Journal of Differential Equations, September 2019, vol. 267, no 6, pp. 3561-3577, https://arxiv.org/abs/1902.07082. [ DOI : 10.1016/j.jde.2019.04.017 ]
https://hal.archives-ouvertes.fr/hal-02024104
[24]
C. Grandmont, M. Hillairet, J. Lequeurre.
Existence of local strong solutions to fluid-beam and fluid-rod interaction systems, in: Annales de l'Institut Henri Poincaré (C) Non Linear Analysis, July 2019, vol. 36, no 4, pp. 1105-1149. [ DOI : 10.1016/j.anihpc.2018.10.006 ]
https://hal.inria.fr/hal-01567661
[25]
B. H. Haak, D. Maity, T. Takahashi, M. Tucsnak.
Mathematical analysis of the motion of a rigid body in a compressible Navier-Stokes-Fourier fluid, in: Mathematical News / Mathematische Nachrichten, 2019, vol. 292, no 9, pp. 1972-2017, https://arxiv.org/abs/1710.08245. [ DOI : 10.1002/mana.201700425 ]
https://hal.archives-ouvertes.fr/hal-01619647
[26]
T. Khajah, X. Antoine, S. P. Bordas.
B-spline FEM for time-harmonic acoustic scattering and propagation, in: Journal of Theoretical and Computational Acoustics, 2019, vol. 27, no 3, 1850059 p. [ DOI : 10.1142/S2591728518500597 ]
https://hal.archives-ouvertes.fr/hal-01377485
[27]
J. Lohéac, T. Takahashi.
Controllability of low Reynolds numbers swimmers of ciliate type, in: ESAIM: Control, Optimisation and Calculus of Variations, 2020, Forthcoming article p, forthcoming. [ DOI : 10.1051/cocv/2019010 ]
https://hal.archives-ouvertes.fr/hal-01569856
[28]
D. Maity, J. San Martín, T. Takahashi, M. Tucsnak.
Analysis of a simplified model of rigid structure floating in a viscous fluid, in: Journal of Nonlinear Science, 2019, vol. 29, no 5, pp. 1975–2020. [ DOI : 10.1007/s00332-019-09536-5 ]
https://hal.archives-ouvertes.fr/hal-01889892
[29]
A. Modave, C. Geuzaine, X. Antoine.
Corner treatments for high-order local absorbing boundary conditions in high-frequency acoustic scattering, in: Journal of Computational Physics, 2020, vol. 401, 109029 p. [ DOI : 10.1016/j.jcp.2019.109029 ]
https://hal.archives-ouvertes.fr/hal-01925160
[30]
B. Obando, T. Takahashi.
Existence of weak solutions for a Bingham fluid-rigid body system, in: Annales de l'Institut Henri Poincaré (C) Non Linear Analysis, 2019. [ DOI : 10.1016/j.anihpc.2018.12.001 ]
https://hal.archives-ouvertes.fr/hal-01942426
[31]
A. Roy, T. Takahashi.
Local null controllability of a rigid body moving into a Boussinesq flow, in: Mathematical Control and Related Fields, 2019, vol. 9, no 4, pp. 793-836. [ DOI : 10.3934/mcrf.2019050 ]
https://hal.archives-ouvertes.fr/hal-01572508
[32]
J. Zhang, D. Li, X. Antoine.
Efficient numerical computation of time-fractional nonlinear Schrödinger equations in unbounded domain, in: Communications in Computational Physics, 2019, vol. 25, no 1, pp. 218-243. [ DOI : 10.4208/cicp.OA-2017-0195 ]
https://hal.archives-ouvertes.fr/hal-01422725

International Conferences with Proceedings

[33]
N. Boussaid, M. Caponigro, T. Chambrion.
On the Ball-Marsden-Slemrod obstruction for bilinear control systems, in: 58 th IEEE Conference on Decision and Control, Nice, France, December 2019, https://arxiv.org/abs/1903.05846.
https://hal.archives-ouvertes.fr/hal-01537743
[34]
T. Chambrion, L. Thomann.
Obstruction to the bilinear control of the Gross-Pitaevskii equation: an example with an unbounded potential, in: Joint 8th IFAC Symposium on Mechatronic Systems and 11th IFAC Symposium on Nonlinear Control Systems, Vienne, Austria, Proceedings of the joint 8th IFAC Symposium on Mechatronic Systems and 11th IFAC Symposium on Nonlinear Control Systems, 2019, vol. 52, no 16, pp. 304 - 309, https://arxiv.org/abs/1903.04185. [ DOI : 10.1016/j.ifacol.2019.11.796 ]
https://hal.archives-ouvertes.fr/hal-02063308

Conferences without Proceedings

[35]
N. Boussaid, M. Caponigro, T. Chambrion.
Impulsive control of the bilinear Schrödinger equation : propagators and attainable sets, in: 58th Conference on Decision and Control, Nice, France, 2019.
https://hal.archives-ouvertes.fr/hal-02074801
[36]
Z. Liu, M. Perrodin, T. Chambrion, R. Stoica.
Modélisation statistique d'un procédé de centrifugation, in: Journées de Statistique, Nancy, France, June 2019.
https://hal.archives-ouvertes.fr/hal-02273932

Other Publications

[37]
S. Ammar, J.-C. Vivalda, B. Zitouni.
Strong differential observability for sampled systems, November 2019, working paper or preprint.
https://hal.inria.fr/hal-02377400
[38]
X. Antoine, F. Fillion-Gourdeau, E. Lorin, S. McLean.
Pseudospectral computational methods for the time-dependent Dirac equation in static curved spaces, October 2019, https://arxiv.org/abs/1909.02894 - working paper or preprint.
https://hal.archives-ouvertes.fr/hal-02340827
[39]
X. Antoine, C. Geuzaine, Q. Tang.
Perfectly Matched Layer for computing the dynamics of nonlinear Schrödinger equations by pseudospectral methods. Application to rotating Bose-Einstein condensates, October 2019, working paper or preprint.
https://hal.archives-ouvertes.fr/hal-02340832
[40]
X. Antoine, E. Lorin.
Double-preconditioning for Fractional Linear Systems. Application to Stationary Fractional Partial Differential Equations, October 2019, working paper or preprint.
https://hal.archives-ouvertes.fr/hal-02340820
[41]
X. Antoine, E. Lorin.
ODE-based Double-preconditioning for Solving Linear Systems Aαx=b and f(A)x=b, October 2019, working paper or preprint.
https://hal.archives-ouvertes.fr/hal-02340590
[42]
M. Badra, T. Takahashi.
Gevrey regularity for a system coupling the Navier-Stokes system with a beam: the non-flat case, October 2019, working paper or preprint.
https://hal.archives-ouvertes.fr/hal-02303258
[43]
R. Bunoiu, L. Chesnel, K. Ramdani, M. Rihani.
Homogenization of Maxwell's equations and related scalar problems with sign-changing coefficients, December 2019, working paper or preprint.
https://hal.inria.fr/hal-02421312
[44]
E. Cerpa, E. Crépeau, J. Valein.
Boundary controllability of the Korteweg-de Vries equation on a tree-shaped network, May 2019, working paper or preprint.
https://hal.archives-ouvertes.fr/hal-02137907
[45]
A. Duca.
Bilinear quantum systems on compact graphs: well-posedness and global exact controllability, June 2019, working paper or preprint.
https://hal.archives-ouvertes.fr/hal-01830297
[46]
A. Duca.
Simultaneous global exact controllability in projection of infinite 1D bilinear Schrödinger equations, June 2019, working paper or preprint.
https://hal.archives-ouvertes.fr/hal-01481873
[47]
M. Ghattassi, T.-M. Laleg, J.-C. Vivalda.
Analysis and Output Tracking Design for the Direct Contact Membrane distillation system, November 2019, https://arxiv.org/abs/1902.00964 - 33 pages, 3 figures.
https://hal.archives-ouvertes.fr/hal-02368695
[48]
M. Hillairet, T. Takahashi.
Existence of contacts for the motion of a rigid body into a viscous incompressible fluid with the Tresca boundary conditions, December 2019, working paper or preprint.
https://hal.archives-ouvertes.fr/hal-02393058
[49]
A. Lieu, P. Marchner, G. Gabard, H. Beriot, X. Antoine, C. Geuzaine.
A Non-Overlapping Schwarz Domain Decomposition Method with High-Order Finite Elements for Flow Acoustics, November 2019, working paper or preprint.
https://hal.archives-ouvertes.fr/hal-02371050
[50]
D. Maity, T. Takahashi.
Lp theory for the interaction between the incompressible Navier-Stokes system and a damped beam, September 2019, working paper or preprint.
https://hal.archives-ouvertes.fr/hal-02294097
[51]
A. Modave, A. Royer, X. Antoine, C. Geuzaine.
An optimized Schwarz domain decomposition method with cross-point treatment for time-harmonic acoustic scattering, January 2020, working paper or preprint.
https://hal.archives-ouvertes.fr/hal-02432422
[52]
G. Pang, Y. Yang, X. Antoine, S. Tang.
Stability and convergence analysis of artificial boundary conditions for the Schrödinger equation on a rectangular domain, October 2019, working paper or preprint.
https://hal.archives-ouvertes.fr/hal-02340837
[53]
P. S. Petrov, X. Antoine.
Pseudodifferential adiabatic mode parabolic equations in curvilinear coordinates and their numerical solution, November 2019, working paper or preprint.
https://hal.archives-ouvertes.fr/hal-02342637
[54]
A. Roy, T. Takahashi.
Stabilization of a rigid body moving in a compressible viscous fluid, October 2019, working paper or preprint.
https://hal.archives-ouvertes.fr/hal-02314870
[55]
J. Valein.
Stabilization of the Korteweg-de Vries equation with internal time-delay feedback, February 2019, working paper or preprint.
https://hal.archives-ouvertes.fr/hal-02020757
References in notes
[56]
C. Alves, A. L. Silvestre, T. Takahashi, M. Tucsnak.
Solving inverse source problems using observability. Applications to the Euler-Bernoulli plate equation, in: SIAM J. Control Optim., 2009, vol. 48, no 3, pp. 1632-1659.
[57]
X. Antoine, K. Ramdani, B. Thierry.
Wide Frequency Band Numerical Approaches for Multiple Scattering Problems by Disks, in: Journal of Algorithms & Computational Technologies, 2012, vol. 6, no 2, pp. 241–259.
[58]
X. Antoine, C. Geuzaine, K. Ramdani.
Computational Methods for Multiple Scattering at High Frequency with Applications to Periodic Structures Calculations, in: Wave Propagation in Periodic Media, Progress in Computational Physics, Vol. 1, Bentham, 2010, pp. 73-107.
[59]
D. Auroux, J. Blum.
A nudging-based data assimilation method : the Back and Forth Nudging (BFN) algorithm, in: Nonlin. Proc. Geophys., 2008, vol. 15, no 305-319.
[60]
M. I. Belishev, S. A. Ivanov.
Reconstruction of the parameters of a system of connected beams from dynamic boundary measurements, in: Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI), 2005, vol. 324, no Mat. Vopr. Teor. Rasprostr. Voln. 34, pp. 20–42, 262.
[61]
M. Bellassoued, D. Dos Santos Ferreira.
Stability estimates for the anisotropic wave equation from the Dirichlet-to-Neumann map, in: Inverse Probl. Imaging, 2011, vol. 5, no 4, pp. 745–773.
http://dx.doi.org/10.3934/ipi.2011.5.745
[62]
M. Bellassoued, D. D. S. Ferreira.
Stable determination of coefficients in the dynamical anisotropic Schrödinger equation from the Dirichlet-to-Neumann map, in: Inverse Problems, 2010, vol. 26, no 12, 125010, 30 p.
http://dx.doi.org/10.1088/0266-5611/26/12/125010
[63]
Y. Boubendir, X. Antoine, C. Geuzaine.
A Quasi-Optimal Non-Overlapping Domain Decomposition Algorithm for the Helmholtz Equation, in: Journal of Computational Physics, 2012, vol. 2, no 231, pp. 262-280.
[64]
M. Boulakia.
Existence of weak solutions for an interaction problem between an elastic structure and a compressible viscous fluid, in: J. Math. Pures Appl. (9), 2005, vol. 84, no 11, pp. 1515–1554.
http://dx.doi.org/10.1016/j.matpur.2005.08.004
[65]
M. Boulakia, S. Guerrero.
Regular solutions of a problem coupling a compressible fluid and an elastic structure, in: J. Math. Pures Appl. (9), 2010, vol. 94, no 4, pp. 341–365.
http://dx.doi.org/10.1016/j.matpur.2010.04.002
[66]
M. Boulakia, A. Osses.
Local null controllability of a two-dimensional fluid-structure interaction problem, in: ESAIM Control Optim. Calc. Var., 2008, vol. 14, no 1, pp. 1–42.
http://dx.doi.org/10.1051/cocv:2007031
[67]
M. Boulakia, E. Schwindt, T. Takahashi.
Existence of strong solutions for the motion of an elastic structure in an incompressible viscous fluid, in: Interfaces Free Bound., 2012, vol. 14, no 3, pp. 273–306.
http://dx.doi.org/10.4171/IFB/282
[68]
G. Bruckner, M. Yamamoto.
Determination of point wave sources by pointwise observations: stability and reconstruction, in: Inverse Problems, 2000, vol. 16, no 3, pp. 723–748.
[69]
A. Chambolle, B. Desjardins, M. J. Esteban, C. Grandmont.
Existence of weak solutions for the unsteady interaction of a viscous fluid with an elastic plate, in: J. Math. Fluid Mech., 2005, vol. 7, no 3, pp. 368–404.
http://dx.doi.org/10.1007/s00021-004-0121-y
[70]
T. Chambrion, A. Munnier.
Locomotion and control of a self-propelled shape-changing body in a fluid, in: J. Nonlinear Sci., 2011, vol. 21, no 3, pp. 325–385.
http://dx.doi.org/10.1007/s00332-010-9084-8
[71]
T. Chambrion, A. Munnier.
Generic controllability of 3D swimmers in a perfect fluid, in: SIAM J. Control Optim., 2012, vol. 50, no 5, pp. 2814–2835.
http://dx.doi.org/10.1137/110828654
[72]
C. Choi, G. Nakamura, K. Shirota.
Variational approach for identifying a coefficient of the wave equation, in: Cubo, 2007, vol. 9, no 2, pp. 81–101.
[73]
C. Conca, J. San Martín, M. Tucsnak.
Existence of solutions for the equations modelling the motion of a rigid body in a viscous fluid, in: Comm. Partial Differential Equations, 2000, vol. 25, no 5-6, pp. 1019–1042.
http://dx.doi.org/10.1080/03605300008821540
[74]
D. Coutand, S. Shkoller.
Motion of an elastic solid inside an incompressible viscous fluid, in: Arch. Ration. Mech. Anal., 2005, vol. 176, no 1, pp. 25–102.
http://dx.doi.org/10.1007/s00205-004-0340-7
[75]
D. Coutand, S. Shkoller.
The interaction between quasilinear elastodynamics and the Navier-Stokes equations, in: Arch. Ration. Mech. Anal., 2006, vol. 179, no 3, pp. 303–352.
http://dx.doi.org/10.1007/s00205-005-0385-2
[76]
B. Desjardins, M. J. Esteban.
On weak solutions for fluid-rigid structure interaction: compressible and incompressible models, in: Comm. Partial Differential Equations, 2000, vol. 25, no 7-8, pp. 1399–1413.
http://dx.doi.org/10.1080/03605300008821553
[77]
B. Desjardins, M. J. Esteban.
Existence of weak solutions for the motion of rigid bodies in a viscous fluid, in: Arch. Ration. Mech. Anal., 1999, vol. 146, no 1, pp. 59–71.
http://dx.doi.org/10.1007/s002050050136
[78]
B. Desjardins, M. J. Esteban, C. Grandmont, P. Le Tallec.
Weak solutions for a fluid-elastic structure interaction model, in: Rev. Mat. Complut., 2001, vol. 14, no 2, pp. 523–538.
[79]
A. El Badia, T. Ha-Duong.
Determination of point wave sources by boundary measurements, in: Inverse Problems, 2001, vol. 17, no 4, pp. 1127–1139.
[80]
M. El Bouajaji, X. Antoine, C. Geuzaine.
Approximate Local Magnetic-to-Electric Surface Operators for Time-Harmonic Maxwell's Equations, in: Journal of Computational Physics, 2015, vol. 15, no 279, pp. 241-260.
[81]
M. El Bouajaji, B. Thierry, X. Antoine, C. Geuzaine.
A quasi-optimal domain decomposition algorithm for the time-harmonic Maxwell's equations, in: Journal of Computational Physics, 2015, vol. 294, no 1, pp. 38-57. [ DOI : 10.1016/j.jcp.2015.03.041 ]
https://hal.archives-ouvertes.fr/hal-01095566
[82]
E. Feireisl.
On the motion of rigid bodies in a viscous compressible fluid, in: Arch. Ration. Mech. Anal., 2003, vol. 167, no 4, pp. 281–308.
http://dx.doi.org/10.1007/s00205-002-0242-5
[83]
E. Feireisl.
On the motion of rigid bodies in a viscous incompressible fluid, in: J. Evol. Equ., 2003, vol. 3, no 3, pp. 419–441, Dedicated to Philippe Bénilan.
http://dx.doi.org/10.1007/s00028-003-0110-1
[84]
E. Feireisl, M. Hillairet, Š. Nečasová.
On the motion of several rigid bodies in an incompressible non-Newtonian fluid, in: Nonlinearity, 2008, vol. 21, no 6, pp. 1349–1366.
http://dx.doi.org/10.1088/0951-7715/21/6/012
[85]
E. Fridman.
Observers and initial state recovering for a class of hyperbolic systems via Lyapunov method, in: Automatica, 2013, vol. 49, no 7, pp. 2250 - 2260.
[86]
G. P. Galdi, A. L. Silvestre.
On the motion of a rigid body in a Navier-Stokes liquid under the action of a time-periodic force, in: Indiana Univ. Math. J., 2009, vol. 58, no 6, pp. 2805–2842.
http://dx.doi.org/10.1512/iumj.2009.58.3758
[87]
O. Glass, F. Sueur.
The movement of a solid in an incompressible perfect fluid as a geodesic flow, in: Proc. Amer. Math. Soc., 2012, vol. 140, no 6, pp. 2155–2168.
http://dx.doi.org/10.1090/S0002-9939-2011-11219-X
[88]
C. Grandmont, Y. Maday.
Existence for an unsteady fluid-structure interaction problem, in: M2AN Math. Model. Numer. Anal., 2000, vol. 34, no 3, pp. 609–636.
http://dx.doi.org/10.1051/m2an:2000159
[89]
G. Haine.
Recovering the observable part of the initial data of an infinite-dimensional linear system with skew-adjoint generator, in: Mathematics of Control, Signals, and Systems, 2014, vol. 26, no 3, pp. 435-462.
[90]
G. Haine, K. Ramdani.
Reconstructing initial data using observers: error analysis of the semi-discrete and fully discrete approximations, in: Numer. Math., 2012, vol. 120, no 2, pp. 307-343.
[91]
J. Houot, A. Munnier.
On the motion and collisions of rigid bodies in an ideal fluid, in: Asymptot. Anal., 2008, vol. 56, no 3-4, pp. 125–158.
[92]
O. Y. Imanuvilov, T. Takahashi.
Exact controllability of a fluid-rigid body system, in: J. Math. Pures Appl. (9), 2007, vol. 87, no 4, pp. 408–437.
http://dx.doi.org/10.1016/j.matpur.2007.01.005
[93]
V. Isakov.
Inverse problems for partial differential equations, Applied Mathematical Sciences, Second, Springer, New York, 2006, vol. 127.
[94]
N. V. Judakov.
The solvability of the problem of the motion of a rigid body in a viscous incompressible fluid, in: Dinamika Splošn. Sredy, 1974, no Vyp. 18 Dinamika Zidkost. so Svobod. Granicami, pp. 249–253, 255.
[95]
B. Kaltenbacher, A. Neubauer, O. Scherzer.
Iterative regularization methods for nonlinear ill-posed problems, Radon Series on Computational and Applied Mathematics, Walter de Gruyter GmbH & Co. KG, Berlin, 2008, vol. 6.
[96]
G. Legendre, T. Takahashi.
Convergence of a Lagrange-Galerkin method for a fluid-rigid body system in ALE formulation, in: M2AN Math. Model. Numer. Anal., 2008, vol. 42, no 4, pp. 609–644.
http://dx.doi.org/10.1051/m2an:2008020
[97]
J. Lequeurre.
Existence of strong solutions to a fluid-structure system, in: SIAM J. Math. Anal., 2011, vol. 43, no 1, pp. 389–410.
http://dx.doi.org/10.1137/10078983X
[98]
J. Lohéac, A. Munnier.
Controllability of 3D Low Reynolds Swimmers, in: ESAIM:COCV, 2013.
[99]
D. Luenberger.
Observing the state of a linear system, in: IEEE Trans. Mil. Electron., 1964, vol. MIL-8, pp. 74-80.
[100]
P. Moireau, D. Chapelle, P. Le Tallec.
Joint state and parameter estimation for distributed mechanical systems, in: Computer Methods in Applied Mechanics and Engineering, 2008, vol. 197, pp. 659–677.
[101]
A. Munnier, B. Pinçon.
Locomotion of articulated bodies in an ideal fluid: 2D model with buoyancy, circulation and collisions, in: Math. Models Methods Appl. Sci., 2010, vol. 20, no 10, pp. 1899–1940.
http://dx.doi.org/10.1142/S0218202510004829
[102]
A. Munnier, E. Zuazua.
Large time behavior for a simplified N-dimensional model of fluid-solid interaction, in: Comm. Partial Differential Equations, 2005, vol. 30, no 1-3, pp. 377–417.
http://dx.doi.org/10.1081/PDE-200050080
[103]
J. O'Reilly.
Observers for linear systems, Mathematics in Science and Engineering, Academic Press Inc., Orlando, FL, 1983, vol. 170.
[104]
J. Ortega, L. Rosier, T. Takahashi.
On the motion of a rigid body immersed in a bidimensional incompressible perfect fluid, in: Ann. Inst. H. Poincaré Anal. Non Linéaire, 2007, vol. 24, no 1, pp. 139–165.
http://dx.doi.org/10.1016/j.anihpc.2005.12.004
[105]
K. Ramdani, M. Tucsnak, G. Weiss.
Recovering the initial state of an infinite-dimensional system using observers, in: Automatica, 2010, vol. 46, no 10, pp. 1616-1625.
[106]
J.-P. Raymond.
Feedback stabilization of a fluid-structure model, in: SIAM J. Control Optim., 2010, vol. 48, no 8, pp. 5398–5443.
http://dx.doi.org/10.1137/080744761
[107]
J. San Martín, J.-F. Scheid, L. Smaranda.
A modified Lagrange-Galerkin method for a fluid-rigid system with discontinuous density, in: Numer. Math., 2012, vol. 122, no 2, pp. 341–382.
http://dx.doi.org/10.1007/s00211-012-0460-1
[108]
J. San Martín, J.-F. Scheid, L. Smaranda.
The Lagrange-Galerkin method for fluid-structure interaction problems, in: Boundary Value Problems., 2013, pp. 213–246.
[109]
J. San Martín, J.-F. Scheid, T. Takahashi, M. Tucsnak.
Convergence of the Lagrange-Galerkin method for the equations modelling the motion of a fluid-rigid system, in: SIAM J. Numer. Anal., 2005, vol. 43, no 4, pp. 1536–1571 (electronic).
http://dx.doi.org/10.1137/S0036142903438161
[110]
J. San Martín, J.-F. Scheid, T. Takahashi, M. Tucsnak.
An initial and boundary value problem modeling of fish-like swimming, in: Arch. Ration. Mech. Anal., 2008, vol. 188, no 3, pp. 429–455.
http://dx.doi.org/10.1007/s00205-007-0092-2
[111]
J. San Martín, L. Smaranda, T. Takahashi.
Convergence of a finite element/ALE method for the Stokes equations in a domain depending on time, in: J. Comput. Appl. Math., 2009, vol. 230, no 2, pp. 521–545.
http://dx.doi.org/10.1016/j.cam.2008.12.021
[112]
J. San Martín, V. Starovoitov, M. Tucsnak.
Global weak solutions for the two-dimensional motion of several rigid bodies in an incompressible viscous fluid, in: Arch. Ration. Mech. Anal., 2002, vol. 161, no 2, pp. 113–147.
http://dx.doi.org/10.1007/s002050100172
[113]
J.-F. Scheid, J. Sokolowski.
Shape optimization for a fluid-elasticity system, in: Pure and Applied Functional Analysis, 2018, vol. 3, no 1, pp. 193-217.
https://hal.archives-ouvertes.fr/hal-01449478
[114]
D. Serre.
Chute libre d'un solide dans un fluide visqueux incompressible. Existence, in: Japan J. Appl. Math., 1987, vol. 4, no 1, pp. 99–110.
http://dx.doi.org/10.1007/BF03167757
[115]
P. Stefanov, G. Uhlmann.
Thermoacoustic tomography with variable sound speed, in: Inverse Problems, 2009, vol. 25, no 7, 16 p, 075011.
[116]
T. Takahashi.
Analysis of strong solutions for the equations modeling the motion of a rigid-fluid system in a bounded domain, in: Adv. Differential Equations, 2003, vol. 8, no 12, pp. 1499–1532.
[117]
H. Trinh, T. Fernando.
Functional observers for dynamical systems, Lecture Notes in Control and Information Sciences, Springer, Berlin, 2012, vol. 420.
[118]
J. L. Vázquez, E. Zuazua.
Large time behavior for a simplified 1D model of fluid-solid interaction, in: Comm. Partial Differential Equations, 2003, vol. 28, no 9-10, pp. 1705–1738.
http://dx.doi.org/10.1081/PDE-120024530
[119]
H. F. Weinberger.
On the steady fall of a body in a Navier-Stokes fluid, in: Partial differential equations (Proc. Sympos. Pure Math., Vol. XXIII, Univ. California, Berkeley, Calif., 1971), Providence, R. I., Amer. Math. Soc., 1973, pp. 421–439.