Research interests: inverse problems, control of PDEs

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Publications

Submitted

- Immersed Boundary Method for the Complete Electrode Model in Electrical Impedance Tomography, with N. Nasr and L. Weynans. hal, arXiv.

- Null-controllability properties of the generalized two-dimensional Baouendi-Grushin equation with non-rectangular control sets, with A. Koenig and J. Royer. hal, arXiv.

Accepted and/or published

♫ The Morozov’s principle applied to data assimilation problems, with L. Bourgeois. ESAIM: Mathematical Modelling and Numerical Analysis. www, hal, arXiv.

♫ A unified strategy for observability of waves in an annulus with various boundary conditions, avec L. Baudouin , S. Ervedoza and A. Mercado. Mathematical Reports. www, hal.

♫ Contact Adapting Electrode Model for Electrical Impedance Tomography, with N. Hyvönen, T. Kuutela, T. Valkonen. SIAM Journal on Applied Mathematics. www, hal, arXiv.

♫ Uniform null controllability for parabolic equations with discontinuous diffusion coefficients, avec S. Ervedoza et R. Morales. Control, Optimisation and Calculus of Variations. www, hal.

♫ Critical time for the observability of Kolmogorov-type equations, with J. Royer. Journal de l'École Polytechnique. www, hal, arXiv.

♫ Monotonicity-based reconstruction of extreme inclusions in electrical impedance tomography, with V. Candiani, H. Garde and N. Hyvönen. SIAM Journal on Mathematical Analysis. www, hal, arXiv.

♫ A dual approach to Kohn-Vogelius regularization applied to data completion problems, with F. Caubet. Inverse Problems. www, pdf, hal.

♫ Backward uniqueness results for some parabolic equations in an infinite rod, with S. Ervedoza. Mathematical Control and Related Fields. www, hal.

♫ Minimal time issues for observability of Grushin-type equations, with K. Beauchard and S. Ervedoza. Annales de l'Institut Fourier. www, hal.

♫ On the cost of observability in small times for the one-dimensional heat equation, with S. Ervedoza. Analysis & PDE. www, hal.

♫ The inverse obstacle problem for the wave equation in finite time domain, with L. Bourgeois and D. Ponomarev. Inverse Problems and Imaging. www, hal.

♫ On the reachable set for the one-dimensional heat equation, with S. Ervedoza. SIAM Journal on Control and Optimization. www, pdf, hal, arXiv.

♫ On the data completion problem and the inverse obstacle problem with partial Cauchy data for Laplace's equation, with F. Caubet and M. Godoy. Control, Optimisation and Calculus of Variations. hal, www.

♫ The "exterior approach" applied to the inverse obstacle problem for the heat equation, with L. Bourgeois. SIAM Journal on Numerical Analysis. hal, arXiv, pdf, www.

♫ Stability estimates for Navier-Stokes equations and application to inverse problems, with M. Badra and F. Caubet. Discrete and Continuous Dynamical System. www, hal, arXiv, pdf.

♫ Iterated quasi-reversibility method applied to elliptic and parabolic data completion problems. Inverse Problems and Imaging. hal, arXiv, www.

♫ Electrode modeling: the effect of contact impedance, with S. Staboulis. ESAIM: Mathematical Modelling and Numerical Analysis. www, arXiv.

♫ Application of mixed fomulations of quasi-reversibility to solve ill-posed problems for heat and wave equations: the 1d case, with E. Bécache, L. Bourgeois, and L. Franceschini. Inverse Problems and Imaging. www, pdf.

♫ The "exterior approach" to solve the inverse obstacle problem for the Stokes system, with L. Bourgeois. Inverse Problems and Imaging. www, pdf.

♫ An Hdiv-based mixed quasi-reversibility method for solving elliptic Cauchy problems, with A. Hannukainen and N. Hyvönen. SIAM Journal on Numerical Analysis. www, pdf.

♫ Simultaneous recovery of admittivity and body shape in electrical impedance tomography: an experimental evaluation, with N. Hyvönen, A. Seppänen and S. Staboulis. Inverse Problems. www.

♫ Simultaneous reconstruction of outer boundary shape and conductivity distribution in electrical impedance tomography, with N. Hyvönen, A. Seppänen and S. Staboulis. SIAM Journal on Imaging Sciences. arXiv, www.

♫ Fine-Tuning electrode information in electrical impedance tomography, with H. Hakula, N. Hyvönen & S. Staboulis. Inverse Problems and Imaging. www, pdf.

♫ The "exterior approach": a new framework to solve inverse obstacle problems. Inverse Problems. www, pdf.

♫ About identification of defects in an elastic-plastic medium from boundary measurements in the antiplane case, with L. Bourgeois. Applicable Analysis. www, pdf.

♫ A quasi-reversibility approach to solve the inverse obstacle problem, with L. Bourgeois. Inverse problems and imaging. www, pdf.

♫ About stability and regularization of ill-posed elliptic Cauchy problems: the case of Lipschitz domains, with L. Bourgeois. Applicable Analysis. www, pdf.

♫ A duality-based method of quasi-reversibility to solve the Cauchy problem in the presence of noisy data, with L. Bourgeois. Inverse Problems. www, pdf.

Thesis

Méthodes de quasi-réversiblité et de lignes de niveau appliquées aux problèmes inverses elliptiques, under the supervision of François Jouve and Laurent Bourgeois.

Presentations

- October 2022: Null-controllability properties of the generalized two-dimensional Baouendi-Grushin equation, Workshop on Control Problems, Dortmund University.

- January 2022: The Morozov’s principle applied to data assimilation problems, Séminaire du Laboratoire de Modélisation Mathématique et Numérique dans les Sciences de l’Ingénieur, ENIT, Tunis.

- November 2021 : Minimal time issues for the observability of bidimensional Grushin and Kolmogorov equations, workshop Inverse Problems and Related Fields, Fédération de Recherche des Unités de Mathématiques de Marseille.

- March 2021 : Electrical impedance tomography with imprecisely known geometry, Séminaire de Modélisation et Calcul Scientifique, Laboratoire Analyse, Géométrie et Applications, Université Sorbonne Paris Nord.

- March 2021 : Temps minimal d'observabilité pour Kolmogorov, Groupe de travail Contrôle, Institut de Mathématiques de Toulouse.

- January 2021 : Minimal time issues for the observability of bidimensional Grushin and Kolmogorov equations, Séminaire ANEDP, Laboratoire de Mathématiques d'Orsay.

- January 2020 : Sharp minimal time for the observability of Grushin-type equations, Séminaire MAC, Institut de Mathématiques de Toulouse, Toulouse.

- March 2019 : Sharp minimal time for the observability of Grushin-type equations, Journées EDP de l'IECL, IECL, Metz.

- February 2019: Sharp minimal time for the observability of Grushin-type equations, Séminaire de mathématiques et leurs applications, LMAP, Université de Pau et des pays de l'Adour.

- December 2018: Inverse obstacle problem with partial Cauchy data for the Laplace equation – A shape optimization approach, Workshop Inverse Problems: Theoretical and Numerical Aspects, Laboratoire de Mathématiques de Reims.

- December 2018: Inverse obstacle problem with partial Cauchy data, Workshop IMT-LAAS, LAAS, Toulouse.

- June 2018: Exterior approach for finding defects – the wave equation in finite time domain case, SIAM conference on Imaging Sciences, Bologna, Italy.

- May 2018: Stability estimate for an inverse source problem related to the Grushin equation, 9th International Conference Inverse Problems: Modeling and Simulation, Malta.

- November 2017: Simultaneous reconstruction of outer boundary shape and conductivity in electrical impedance tomography, groupe de travail Optimisation de Forme (Shape Optimization), Laboratoire de Mathématiques et de leurs Applications, Pau.

- August 2017: Inverse obstacle problem with partial Cauchy data: a shape optimization approach, VII Partial differential equations, optimal design and numerics, Benasque, Spain.

- December 2016: On the reachable set of the 1-d heat equation, Workshop Apache, Toulouse.

- November 2016: On the reachable set of the 1-d heat equation, Séminaire de l'équipe MIP, Institut de Mathématiques de Toulouse, Toulouse.

- November 2016: On the reachable set of the 1-d heat equation, Workshop Carleman Estimates, Unique Continuation and Applications, University College London, Londres, Royaume-Uni.

- June 2016: Inverse obstacle problem with partial Cauchy data: a shape optimization approach, Mini-symposium Applications of shape and structural optimization, Inverse Problems, Control and Shape Optimization (PICOF'16), Autrans.

- May 2016: Iterated quasi-reversibility: application to elliptic and parabolic data completion problems, Mini-Symposium Aspects numériques de la contrôlabilité des EDPs et problèmes inverses, Congrès National d'Analyse Numérique 2016, Obernai.

- May 2015: Exterior approach to inclusion detection in a parabolic inverse boundary value problem, Applied Inverse Problems Conference 2015, university of Helsinki, Helsinki, Finlande.

- October 2014: The exterior approach applied to the inverse obstacle problem for the heat equation, conférence Contrôle, Problèmes inverses et Applications, Université Blaise Pascal, Clermont-Ferrand.

- May 2014: Simultaneous reconstruction of outer boundary shape and conductivity in electrical impedance tomography, Séminaire de l'équipe DEFI, Inria-Saclay.

- November 2013: The exterior approach applied to the inverse obstacle problem for the Stokes system, Workshop Problèmes Inverses, FRUMAM, Marseille.

- July 2013: A mixed formulation of quasi-reversibility: application to the reconstruction of perfectly conducting inclusions in EIT, Applied Inverse Problems Conference, KAIST, Daejon, Corée.

- October 2012: L' "approche par l'extérieur" pour résoudre des problèmes inverses d'obstacle. Séminaire de l'équipe Mathématiques pour l'Industrie et la Physique, Institut de Mathématiques de Toulouse, UPS-Toulouse III.

- April 2012: A mixed formulation of the quasi-reversibility method, Inverse Problems, Control and Shape Optimization (PICOF'12), École Polytechnique, Palaiseau.

- April 2012: Une formulation mixte de la méthode de quasi-réversibilité pour résoudre des problèmes de complétion de données et de reconstruction d’obstacles, Séminaire Sciences Numériques pour la Mécanique, LMSSMat, École Centrale Paris.

- December 2011: A mixed formulation of the quasi-reversibility method to solve elliptic Cauchy problems in 2d and 3d, Journées Lions-Magenes, Laboratoire Jacques-Louis Lions, Paris.

- May 2011: The exterior approach to solve an inverse obstacle problem in electric impedance tomography, Applied Inverse Problems Conference, College Station, Texas.

- February 2011: A new framework to solve the inverse obstacle problem: the "exterior approach", Inverse problems seminars, Inverse problems research group, University of Helsinki, Finlande

- February 2011: A new framework to solve the inverse obstacle problem: the "exterior approach", Seminar on numerical analysis and computational science, Department of Mathematics and Systems Analysis, Aalto University, Espoo, Finlande

- January 2011: Quasi-reversibility and level-set methods applied to elliptic inverse problems, Groupe de travail EDP, Laboratoire de Mathématiques et Applications de Metz, Université Paul Verlaine , Metz

- June 2010: Une méthode level-set pour résoudre le problème inverse de l'obstacle, Congrès National d'Analyse Numérique 2010, Carcans-Maubuisson

- May 2010: On identification of defects from boundary measurements: the case of elastoplastic media, IV European Conference on Computational Mechanics, Paris

- March 2010: A duality-based method to solve the Cauchy problem in presence of noisy data (Poster), MMNS Workshop Inverse problems for Waves: Methods and Applications, Palaiseau

- November 2009: Couplage méthode de quasi-réversibilité/level-set pour la résolution du problème inverse de l'obstacle, Séminaire POems, ENSTA-INRIA Rocquencourt

- October 2009: Couplage méthode de quasi-réversibilité/level-set pour la résolution du problème inverse de l'obstacle, Séminaire DeFI, INRIA Saclay