UMA Home page for Laurent Bourgeois
Teaching/Research
Ingénieur de l'Armement
Ingénieur de l'Armement
Research Habilitation 2012
Ph.D. 1998
EMAIL_TEMPLATE
Research activities
Inverse problems, regularization of ill-posed problems. More precisely :
- wave diffraction problems,
- method of quasi-reversibility to solve ill-posed Cauchy problems and application to inverse problems,
- inverse problems related to mechanics of materials,
- inverse scattering in waveguides with sampling methods,
- inverse scattering for generalized impedance boundary conditions,
- uniqueness and stability of ill-posed problems, in particular with Carleman estimates.
Students :
- Jérémi Dardé (PHD, advisor with F. Jouve)
- Nicolas Chaulet (PHD, advisor with H. Haddar)
- Arnaud Recoquillay (PHD, advisor with V. Baronian)
- Jean-François Fritsch (PHD, advisor with C. Hazard)
- Frédérique Le Louer (Post-doc, advisor with E. Lunéville)
- Anne-Claire Egloffe (Post-doc, advisor with E. Lunéville)
- Dmitry Ponomarev (Post-doc)
Teaching activities
ENSTA : Basic analysis for partial differential equations,
Optimal control of partial differential equations,
Fonctions of complex variable,
Non-linear materials,
Inverse Problems : mathematical analysis and numerical methods (Master 2)
Inverse problems governed by PDEs (Master 2)
Publications
Papers in peer-reviewed journals
Submitted
- Generalized impedance boundary conditions with vanishing or sign-changing impedance
and
submitted [
] 
2023
- Scattering in a partially open waveguide: the forward problem
, , , and
IMA Journal of Applied Maths, feb, 2023 [ ] 
- Scattering in a partially open waveguide: the inverse problem
, and
Inverse Problems and Imaging, vol. 17/2, pp. 463-489, feb, 2023 [ ]
2022
- The Morozov's principle applied to data assimilation problems
and
M2AN, sep, 2022 [ ]
2021
- Imaging junctions of waveguides
, and
Inverse Problems and Imaging, vol. 15-2, pp. 285--314, feb, 2021 [ ]
2020
- On quasi-reversibility solutions to the Cauchy problem for the Laplace equation: regularity and error estimates
and
M2AN, vol. 54-2, pp. 493-529, feb, 2020 [ ] - On well-posedness of scattering problems in a Kirchhoff-Love infinite plate
and
SIAM Journal of Applied Maths, vol. 80-3, pp. 1546-1566, jun, 2020 [ ] - The Linear Sampling Method for Kirchhoff-Love infinite plates
and
Inverse Problems and Imaging, vol. 14-2, pp. 363-384, apr, 2020 [ ]
2019
- An inverse obstacle problem for the wave equation in a finite time domain
, and
Inverse Problems and Imaging, vol. 13-2, pp. 377-400, apr, 2019 [ ] - On well-posedness of time-harmonic problems in an unbounded strip for a thin plate model
, and
Communications in Mathematical Sciences, vol. 17/6, pp. 1487 – 1529, dec, 2019 [ ]
2018
- A mixed formulation of the Tikhonov regularization and its application to inverse PDE problems
and
M2AN, vol. 52/1, pp. 123-145, jan, 2018 [ ] - Linear Sampling Method applied to Non Destructive Testing of an elastic waveguide: theory, numerics and experiments
, , and
Inverse Problems, vol. 34/7, pp. 075006, jul, 2018 [ ] - On well-posedness of time-harmonic problems in an unbounded strip for a thin plate model
, and
sep, 2018 [ ]
2017
- Quantification of the unique continuation property for the heat equation
Mathematical Control and Related Fields, vol. 7/3, pp. 347-367, sep, 2017 [ ] - The ``exterior approach" applied to the inverse obstacle problem for the heat equation
and
SIAM Journal of Numerical Analysis, vol. 55/4, pp. 1820-1842, 2017 [ ]
2016
- Imaging an acoustic waveguide from surface data in the time domain
, and
Wave Motion, vol. 66, pp. 68-87, nov, 2016 [ ] - Uniqueness results for inverse Robin problems with bounded coefficient
, and
Journal of Functional Analysis, vol. 270/7, pp. 2508-2542, 2016 [ ]
2015
- Application of mixed formulations of quasi-reversibility to solve ill-posed problems for heat and wave equations: the 1D case
, , and
Inverse Problems and Imaging, vol. 9/4, pp. 971-1002, nov, 2015 [ ]
2014
- On the identification of defects in a periodic waveguide from far field data
and
Inverse Problems, vol. 30, pp. 095004, 2014 [ ] - The "exterior approach" to solve the inverse obstacle problem for the Stokes system
and
Inverse Problems and Imaging, vol. 8/1, pp. 23-51, 2014 [ ]
2013
- A remark on Lipschitz stability for inverse problems
C. R. Acad. Sci. Paris, Ser. I, vol. 351, pp. 187-190, 2013 [ ] - On the use of the Linear Sampling Method to identify cracks in elastic waveguides
and
Inverse Problems, vol. 29, pp. 025017, 2013 [ ]
2012
- On simultaneous identification of a scatterer and its generalized impedance boundary condition
, and
Siam Journal of Scientific Computing, vol. 34-3, pp. 1824-1848, 2012 [ ] - On the use of sampling methods to identify cracks in acoustic waveguides
and
Inverse Problems, vol. 28, pp. 105011 (18pp), sep, 2012 [ ]
2011
- About identification of defects in an elastic-plastic medium from boundary measurements in the antiplane case
and
Applicable Analysis, vol. 90/10, pp. 1481-1497, feb, 2011 [ ] - On the use of Lamb modes in the linear sampling method for elastic waveguides
, and
Inverse Problems, vol. 27, pp. 055001(27pp), 2011 [ ] - Stable reconstruction of generalized impedance boundary conditions
, and
Inverse Problems, vol. 27, pp. 095002, 2011 [ ]
2010
- A duality-based method of quasi-reversibility to solve the Cauchy problem in the presence of noisy data
and
Inverse Problems, vol. 26 (9), pp. 095016(21pp), 2010 [ ] - A quasi-reversibility approach to solve the inverse obstacle problem
and
Inverse Problems and Imaging, vol. 4-3, pp. 351-377, 2010 [ ] - About stability and regularization of ill-posed elliptic Cauchy problems: the case of $C^{1,1}$ domains
M2AN, vol. 44 (4), pp. 715-735, 2010 [ ] - About stability and regularization of ill-posed elliptic Cauchy problems: the case of Lipschitz domains
and
Applicable Analysis, vol. 89/11, pp. 1745-1768, 2010 [ ] - Identification of generalized impedance boundary conditions in inverse scattering problems
and
Inverse Problems and Imaging, vol. 4-1, pp. 19-38, 2010 [ ]
2008
- The Linear Sampling Method in a waveguide: a modal formulation
and
Inverse Problems, vol. 24 (1), pp. 015018, 2008 [ ] - The linear sampling method in a waveguide : a formulation based on modes
and
Journal of Physics: Conference Series, vol. 135, pp. 012023, Special Issue : Sixth International Conference on Inverse Problems in Engineering: Theory and Practice (6ICIPE), IOP, 2008 [ ]
2007
- A stability estimate for ill-posed elliptic Cauchy problems in a domain with corners
C. R. Acad. Sci. Paris, Ser. I, vol. 345 (7), pp. 385-390, 2007 [ ] - Locating an obstacle in a 3D finite depth ocean using the convex scattering support
, and
Journal of Computational and Applied Mathematics, vol. 204 (2 SPEC), pp. 387-399, jul, 2007 [ ]
2006
- Convergence rates for the quasi-reversibility method to solve the Cauchy problem for Laplace's equation
Inverse Problems, vol. 22 (2), pp. 413-430, 2006 [ ]
2005
- A mixed formulation of quasi-reversibility to solve the Cauchy problem for Laplace's equation
Inverse Problems, vol. 21 (3), pp. 1087-1104, 2005 [ ]
2000
- An inverse approach to determine the non-linear properties of induction heat-treated steels
and
Eur. J. Mech. A/Solids, vol. 19, pp. 69-88, 2000
1996
- Incompressible fibre-reinforced composites : Effective elastoplastic or viscoelastic behaviour
, and
pp. 132-139, Continuum Models and Discrete Systems, Markov K., 1996
International conferences with proceedings
2011
- Stability results for the identification of generalized impedance boundary coeficients
, and
Waves 2011, Vancouver, jul, 2011 [ ]
2008
- The method of quasi-reversibility to solve the Cauchy problems for elliptic partial differential equations
and
PAMM, vol. 7, pp. 104201-104202, Special Issue : Sixth International Congress on Industrial Applied Mathematics (ICIAM07), Wiley, 2008 [ ]
Conferences without proceedings
2019
- Imaging a waveguide: the importance of using modes
, , and
NCMIP Conference, 24/5/2019, ENS Cachan, may, 2019 - Mixed quasi-reversibility approaches to identify obstacles in an acoustic waveguide
and
Worshop Problèmes Inverses, 6-7/5/2019, UTC Compiègne, may, 2019 - On well-posedness of scattering problems in a Kirchhoff-Love infinite plate
and
Waves Conference, Vienna, 25-29/08/2019, aug, 2019
2018
- An inverse obstacle problem for the wave equation in a finite time interval
, and
Inverse Problems: Theoretical and Numerical Aspects, Reims, 17-19/12/2018, dec, 2018 - On mixed formulations of quasi-reversibility and their application to inverse obstacle problems
, and
Inverse Problems: Modeling and Simulation, Malta, 21-26/05/2018, may, 2018
2017
- A mixed quasi-reversibility approach to identify obstacles in an acoustic waveguide
and
13th International Conference on Mathematical and Numerical Aspects of Wave Propagation, University of Minnesota, Minneapolis, May 15−19, 2017, 2017
2016
- Imaging an acoustic waveguide from surface data in the time domain
, and
Workshop Inverse Problems for PDEs, Bremen, Allemagne, 29/3-1/4/2016, mar, 2016 - Imaging an acoustic waveguide from surface data in the time domain
, and
New trends in theoretical and numerical analysis of waveguides, Porquerolles, 16-19/05/2016, may, 2016
2015
- Imaging defects in an acoustic waveguide using time-dependent surface data
, and
Ninth meeting of the European Research Network: wave propagation in complex media for quantitative and Non-Destructive Evaluation, dec, 2015 - The inverse Robin problem for bounded coefficient : uniqueness and non-uniqueness results
, and
27th IFIP Conference on System Modelling and Optimization, Sophia Antipolis, 29/6-3/7/2015, jun, 2015 - The inverse Robin problem revisited for non-smooth Robin coefficient
, and
Spectral and Analytic Inverse Problems, IHP, Paris, 4-7/5/2015, may, 2015 - The method of quasi-reversibility for time-dependent wave equation. Application to the inverse obstacle problem
, , and
Inverse Problems in Wave Propagation, Bremen, Allemagne, 7-10/4/2015, apr, 2015
2014
- Inverse scattering in a periodic waveguide from far field data
and
Recent progress in theoretical and numerical aspects of inverse problems, CIRM, Marseille, 19-23/5/2014, may, 2014 - On identification of fixed immersed obstacles in a Stokes fluid from boundary measurements
and
PICOF 2014, Hammamet (Tunisie), 7-9/5/2014, may, 2014
2013
- On Lipschitz stability for a class of inverse problems
Inverse Problems and Nonlinear equations, Ecole Polytechnique, Palaiseau - 22-24/05/2013, may, 2013 - On sampling methods to identify defects in a periodic waveguide from far field data
and
Inverse Problems: Scattering, Tomography and Parameter Identification, Conference honoring Andreas Kirsch for his 60th birthday, Bad Herrenalb - Germany, 8-11/4/2013, apr, 2013 - On the far field of scattering solutions in a periodic waveguide. Part II : The inverse problem
and
Waves conference, Gammarth, Tunisie, 3-7/6/2013, jun, 2013
2012
- An "exterior approach" to solve the inverse obstacle problem for the Stokes system
and
Control of Fluid-Structure Systems and Inverse problems - Toulouse - 25-28/06/2012, jun, 2012 - Reconstruction of a perfectly conducting obstacle coated with a thin dielectric layer
, and
PICOF'12, Palaiseau, France, apr, 2012 - Sur une "approche extérieure" pour résoudre le problème inverse de l'obstacle
and
Journée "Problèmes inverses" - CNAM - 21/06/2012, jun, 2012
2011
- Imaging an elastic waveguide with the Linear Sampling Method by using the Lamb modes
, and
Conférence Applied Inverse Problems 2011, College Station, Texas, 23-27/05/2011, may, 2011
2010
- About quantification of unique continuation for elliptic equations: the case of non-smooth boundary
Trimestre sur le contrôle des EDP et applications, Journée thématique "Inverse Problems", IHP, Paris, 1/10-18/12/2010, nov, 2010 - Coupling quasi-reversibility and level set methods: the inverse obstacle problem revisited
and
Workshop on Inverse Problems for Waves: Methods and Applications, Palaiseau, 29-30/3/2010, 2010 - On identification of defects from boundary measurements : the case of elastoplastic media
and
ECCM 2010 : IV european conference on computational mechanics, 16-21/5/2010, 2010
2009
- Uniqueness and stability for identification of generalized boundary conditions
and
Conférence Applied Inverse Problems 2009, Université de Vienne, Vienne (Autriche), 20-24/7/2009, jul, 2009
2008
- Stabilité conditionnelle pour les problèmes elliptiques mal posés : influence de la régularité du bord
Premier congrès de la SM2A, Rabat (Maroc), 6-8/02/2008, 2008 - The linear sampling method in a waveguide : a formulation based on modes
and
Conférence ICIPE 2008, VVF Dourdan, Dourdan (France), 15-19/6/2008, 2008
2007
- The method of quasi-reversibility to solve the Cauchy problem for elliptic PDE
and
Conférence ICIAM 2007, ETH, Zürich (Suisse), 16-20/7/2007, 2007
2006
- Locating an obstacle in a 3D finite depth ocean using the convex scattering support
, and
Conférence PICOF 2006, Université de Nice, Nice (France), 5-7/4/2006, 2006
2005
- Localisation d'un obstacle dans un océan 3D de profondeur finie
Journées Melina, Le Croisic, 2005 - Locating an obstacle in a 3D waveguide using the scattering support theory
, and
Conférence Waves 2005, Brown University, Providence (USA), 20-24/6/2005, 2005 - Une formulation mixte de la méthode de quasi-réversibilité pour les EDP elliptiques
8èmes Journées d'Analyse Numérique et Optimisation, ENIM, Rabat (Maroc), 14-16/12/2005, 2005
Habilitation these
2012
- Sur quelques problèmes inverses gouvernés par des équations aux dérivées partielles elliptiques
feb, 2012 [ ]
Doctoral these
1998
- Contrôle optimal et problèmes inverses en plasticité
Thèse de l'Ecole Polytechnique, mar, 1998
Research reports
2015
- Uniqueness results for 2D inverse Robin problems with bounded coefficient
, and
jan, 2015 [ ]
2012
- A remark on Lipschitz stability for inverse problems
Rapport INRIA, oct, 2012 [ ]
2011
- On simultaneous identification of a scatterer and its generalized impedance boundary condition
, and
Rapport INRIA, jun, 2011 [ ]
2010
- Identification of generalized impedance boundary conditions: some numerical issues
, and
Rapport INRIA, nov, 2010 [ ]
2009
- Identification of generalized impedance boundary condition in inverse scattering problems
and
Rapport INRIA, 2009 [ ]
2008
- Conditional stability for ill-posed elliptic Cauchy problems : the case of C1,1 domains (part I)
Rapport de recherche INRIA, 2008 [ ] - Conditional stability for ill-posed elliptic Cauchy problems : the case of Lipschitz domains (part II)
and
Rapport de recherche INRIA, sep, 2008 [ ]
Lecture notes
2015
- Imaging a periodic waveguide from far field data
Franco-German Summer School- Inverse Problems for Waves - 24-28/8/2015, aug, 2015
2005
Other publication
2010
- Poster: a duality-based method to solve the Cauchy problem in presence of noisy data.
and
Workshop on Inverse Problems for Waves: Methods and Applications, 2010 [ ]