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Fourier-integral-operator approximation of solutions to first-order hyperbolic pseudodifferential equations I: convergence in Sobolev spaces

Jérôme Le Rousseau
Communications in Partial Differential Equations, 2006, 31, pp.867-906. ⟨10.1080/03605300600635079⟩
Journal articles hal-00003815v3
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Stability of discontinuous diffusion coefficients and initial conditions in an inverse problem for the heat equation

Assia Benabdallah , Patricia Gaitan , Jérôme Le Rousseau
SIAM Journal on Control and Optimization, 2007, 46 (5), pp.1849-1881. ⟨10.1137/050640047⟩
Journal articles hal-00016490v3
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On Carleman estimates for elliptic and parabolic operators. Applications to unique continuation and control of parabolic equations

Jérôme Le Rousseau , Gilles Lebeau
ESAIM: Control, Optimisation and Calculus of Variations, 2012, 18, pp.712-747. ⟨10.1051/cocv/2011168⟩
Journal articles hal-00351736v4
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Carleman estimate for elliptic operators with coefficients with jumps at an interface in arbitrary dimension and application to the null controllability of linear parabolic equations

Jérôme Le Rousseau , Luc Robbiano
Archive for Rational Mechanics and Analysis, 2010, 195, pp.953-990. ⟨10.1007/s00205-009-0242-9⟩
Journal articles hal-00193885v2
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Pseudodifferential multi-product representation of the solution operator of a parabolic equation

Hiroshi Isozaki , Jérôme Le Rousseau
Comm. Partial Differential Equations, 2009, 34 (7), pp.625 - 655. ⟨10.1080/03605300903017330⟩
Journal articles hal-00216207v2
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Fourier-integral operator approximation of solutions to first-order hyperbolic pseudodifferential equations II: microlocal analysis

Jérôme Le Rousseau , Gunther Hormann
Journal de Mathématiques Pures et Appliquées, 2006, 86, pp.403-426. ⟨10.1016/j.matpur.2006.08.004⟩
Journal articles hal-00005759v1
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Discrete Carleman estimates for elliptic operators and uniform controllability of semi-discretized parabolic equations

Franck Boyer , Florence Hubert , Jérôme Le Rousseau
Journal de Mathématiques Pures et Appliquées, 2010, 93 (3), pp.240-273. ⟨10.1016/j.matpur.2009.11.003⟩
Journal articles hal-00366496v2
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Carleman estimates for elliptic operators with complex coefficients Part II: transmission problems

Mourad Bellassoued , Jérôme Le Rousseau
Journal de Mathématiques Pures et Appliquées, 2018, 115, pp.127-186. ⟨10.1016/j.matpur.2018.04.001⟩
Journal articles hal-01312627v1
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Carleman estimates for the one-dimensional heat equation with a discontinuous coefficient and applications to controllability and an inverse problem

Assia Benabdallah , Yves Dermenjian , Jérôme Le Rousseau
Journal of Mathematical Analysis and Applications, 2007, 336 (2), pp.865-887. ⟨10.1016/j.jmaa.2007.03.024⟩
Journal articles hal-00017486v1

Control of partial differential equations

Fatiha Alabau-Boussouira , Roger Brockett , Olivier Glass , Jérôme Le Rousseau , Enrique Zuazua et al.
Cannarsa, Piermarco and Coron, Jean-Michel. Springer, 2048, pp.344, 2012, Lecture Notes in Mathemics
Books hal-00770036v1
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Carleman estimates and controllability results for the one-dimensional heat equation with BV coefficients

Jérôme Le Rousseau
Journal of Differential Equations, 2007, 233, pp.417-447. ⟨10.1016/j.jde.2006.10.005⟩
Journal articles hal-00105669v2
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Uniform null-controllability properties for space/time-discretized parabolic equations

Franck Boyer , Florence Hubert , Jérôme Le Rousseau
Numerische Mathematik, 2011, 118, pp 601-661. ⟨10.1007/s00211-011-0368-1⟩
Journal articles istex hal-00429197v1

On the approximation of the null-controllability problem for parabolic equations

Franck Boyer , Florence Hubert , Jérôme Le Rousseau
18th Conference on Scientific Computing Vysoké Tatry, Mar 2009, Podbanske, Slovakia. pp.101-110
Conference papers hal-00839312v1
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Controllability of two coupled wave equations on a compact manifold

Belhassen Dehman , Jérôme Le Rousseau , Matthieu Léautaud
Archive for Rational Mechanics and Analysis, 2014, 211 (1), pp.113-187. ⟨10.1007/s00205-013-0670-4⟩
Journal articles hal-00686967v2
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Null-controllability of the Kolmogorov equation in the whole phase space

Jérôme Le Rousseau , Iván Moyano
Journal of Differential Equations, 2016, 260, pp.3193-3233. ⟨10.1016/j.jde.2015.09.062⟩
Journal articles hal-01134917v2

Elliptic Carleman Estimates and Applications to Stabilization and Controllability, Volume I

Jérôme Le Rousseau , Gilles Lebeau , Luc Robbiano
Springer International Publishing, 97, 2022, Progress in Nonlinear Differential Equations and Their Applications, ⟨10.1007/978-3-030-88674-5⟩
Books hal-03866673v1
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Carleman estimates for elliptic operators with complex coefficients. Part I: boundary value problems

Mourad Bellassoued , Jérôme Le Rousseau
Journal de Mathématiques Pures et Appliquées, 2015, 104 (4), pp.657-728. ⟨10.1016/j.matpur.2015.03.011⟩
Journal articles hal-00843207v4
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Carleman estimates for stratified media

Assia Benabdallah , Yves Dermenjian , Jérôme Le Rousseau
Journal of Functional Analysis, 2011, 260, pp.3645-3677. ⟨10.1016/j.jfa.2011.02.007⟩
Journal articles hal-00529924v2
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Spectral inequality and resolvent estimate for the bi-Laplace operator

Jérôme Le Rousseau , Luc Robbiano
Journal of the European Mathematical Society, 2020, 22 (4), pp.1003-1094. ⟨10.4171/JEMS/939⟩
Journal articles hal-01194748v5

Elliptic Carleman Estimates and Applications to Stabilization and Controllability, Volume II

Jérôme Le Rousseau , Gilles Lebeau , Luc Robbiano
Springer International Publishing, 98, 2022, Progress in Nonlinear Differential Equations and Their Applications, ⟨10.1007/978-3-030-88670-7⟩
Books hal-03866675v1
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MEASURE PROPAGATION ALONG C^0-VECTOR FIELD AND WAVE CONTROLLABILITY ON A ROUGH COMPACT MANIFOLD

Nicolas Burq , Belhassen Dehman , Jérôme Le Rousseau
2022
Preprints, Working Papers, ... hal-03866679v1
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Carleman estimates and controllability results for the one-dimensional heat equation with {\em BV} coefficients

Jérôme Le Rousseau
Comptes Rendus. Mathématique, 2007, 344 (3), pp.175-180. ⟨10.1016/j.crma.2006.12.011⟩
Journal articles hal-00463330v1
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On the controllability of linear parabolic equations with an arbitrary control location for stratified media

Assia Benabdallah , Yves Dermenjian , Jérôme Le Rousseau
Comptes rendus hebdomadaires des séances de l'Académie des sciences, 2007, 344 (6), pp.357-362. ⟨10.1016/j.crma.2007.01.012⟩
Journal articles hal-00132289v1
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Représentation Microlocale de Solutions de Systèmes Hyperboliques, Application à l'Imagerie, et Contributions au Contrôle et aux Problèmes Inverses pour des Equations Paraboliques

Jérôme Le Rousseau
Mathématiques [math]. Université de Provence - Aix-Marseille I, 2007
Habilitation à diriger des recherches tel-00201887v2
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Controllability of a parabolic system with a diffusive interface

Jérôme Le Rousseau , Matthieu Léautaud , Luc Robbiano
Journal of the European Mathematical Society, 2013, 15 (4), pp.1485-1574. ⟨10.4171/JEMS/397⟩
Journal articles hal-00618234v1
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Geometric control condition for the wave equation with a time-dependent observation domain

Jérôme Le Rousseau , Gilles Lebeau , Peppino Terpolilli , Emmanuel Trélat
Analysis & PDE, 2017, 10 (4), pp.983--1015
Journal articles hal-01342398v2
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Local and global Carleman estimates for parabolic operators with coefficients with jumps at interfaces

Jérôme Le Rousseau , Luc Robbiano
Inventiones Mathematicae, 2011, Vol.183 (2), pp.245-336. ⟨10.1007/s00222-010-0278-3⟩
Journal articles hal-00397223v2
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Carleman estimates for the one-dimensional heat equation with a discontinuous coefficient and applications

Assia Benabdallah , Yves Dermenjian , Jérôme Le Rousseau
Comptes Rendus Mécanique, 2006, 334 (10), pp.582-586. ⟨10.1016/j.crme.2006.07.001⟩
Journal articles hal-00463326v1
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Fourier-integral-operator product representation of solutions to first-order symmetrizable hyperbolic systems

Jérôme Le Rousseau
J. Analyse Math., 2009, 109, pp.81-162. ⟨10.1007/s11854-009-0029-9⟩
Journal articles hal-00194089v2
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On Carleman estimates with two large parameters

Jérôme Le Rousseau
Indiana University Mathematics Journal, 2015, 64, pp.55-113. ⟨10.1512/iumj.2015.64.5397⟩
Journal articles hal-00738717v4