Preprints
M. Choulli, S. Lu and H. Takase, Functional analysis and partial differential equations in spectral Barron spaces. arXiv:2507.06778
M. Choulli, A. Metidji and E. Soccorsi, Determination of the Schrödinger-Robin operator by incomplete or asymptotic spectral boundary data. arXiv:2507.06598
M. Choulli, Upper bound on the multiplicity of eigenvalues of the Schrödinger-Dirichlet operator in dimension two. arXiv:2506.14463
M. Choulli, H. Takase, Quantitative uniqueness of continuation for the Schrödinger equation: explicit dependence on the potential. arXiv:2504.07533
M. Choulli, S. Lu, H. Takase, Stability for an inverse flux and and inverse boundary coefficient problems. arXiv:2502.15406
M. Choulli, H. Takase, Stable determination of the potential for the Helmholtz equation in the high frequency limit from boundary measurements. arXiv:2501.10751
M. Choulli, H. Takase, An inverse obstacle problem for the magnetic Schrödinger equation. arXiv:2411.15792
M. Choulli, H. Takase, New quantitative uniqueness of continuation for elliptic equations. arXiv:2411.03545
M. Choulli, A quantitative Borg-Levinson theorem for a large class of unbounded potentials. arXiv:2410.01346
M. Choulli, Quantitative strong unique continuation property for the Schrödinger operator with unbounded potential. arXiv:2309.0851
M. Choulli, N. Kerraoui and E. Soccorsi, Determining an Iwatsuka Hamiltonian through quantum velocity measurement. arXiv:2305.03320
Books and Lecture notes
M. Choulli, An introduction to the uniqueness of continuation of second order partial differential equations. Lecture notes, to appear.
M. Choulli and M. Yamamoto, Abstract time-fractional Cauchy problems associated to m-dissipative operators. Lecture notes, to appear.
M. Choulli, Une introduction aux séries et intégrales généralisées. EDP Sciences, Paris, 2025.
M. Choulli, Analyse fonctionnnelle appliquée. EDP Sciences, Paris, 2024.
M. Choulli, Analyse fonctionnelle. De Boeck Supérieur, Louvain-la-Neuve, 2022.
M. Choulli, Analyse complexe. De Boeck Supérieur, Louvain-la-Neuve, 2020.
M. Choulli, Applications of elliptric Carleman inequalities to Cauchy and inverse problems. Springer Briefs in Mathematics, Springer, Berlin, 2016.
M. Choulli, Analyse fonctionnelle: équations aux dérivées partielles. Vuibert, Paris, 2013.
M. Choulli, Une introduction aux problèmes inverses elliptiques et paraboliques. Mathématiques et Applications, Vol. 65, Springer-Verlag, Berlin, 2009.
Published or accepted for publication
M. Choulli, Two parabolic inverse problems for an equation with unbounded zero-order coefficient. Inverse Probl. Imaging (2025). arXiv:2411.02901
M. Choulli, Stable determination of the initial data in an IBVP for the wave equation outside a non-trapping obstacle. Commun. Appl. Math. Comput. (2025). arXiv:2401.02364
M. Choulli, Quantitative strong unique continuation for elliptic operators - application to an inverse spectral problem. Front. Math (2025). arXiv:2209.09549
M. Choulli, Correction to “The unique continuation property for second order evolution PDEs” [Partial Differ. Equ. Appl. 2, 67 (2021), 46 p] with additional comments. Partial Differ. Equ. Appl. 6, 33 (2025). arXiv:2005.08475
M. Choulli and M. Yamamoto, Stability of determining a Dirichlet-Laplace-Beltrami operator from its spectral boundary data. Analysis and Applications 23 (6) (2025) 1019-1044. arXiv:2311.18642
M. Choulli and H. Takase, An inverse hyperbolic obstacle problem. J. Evol. Equ. (2025) 25:36. arXiv:2407.05662
M. Choulli and H. Takase, Lipschitz stability for an elliptic inverse problem with two measurements. Res. Math. Sci. (2025) 12:22. arXiv:2404.13901
M. Choulli, Stability inequality for the problem of determining an unbounded potential from boundary measurements. J. Math. Anal. Appl. 547 (2025) 129303. arXiv:2310.17456
M. Choulli and E. M. Ouhabaz, Fractional anisotropic Calderòn problem on complete Riemannian manifolds. Communications in Contemporary Mathematics 26, (9) (2024) 2350057. arXiv:2303.03764
M. Choulli, A. Metidji and E. Soccorsi, Multidimensional Borg-Levinson type analysis of the Robin Laplacian with unbounded potentials. Doc. Math. 29 (4) (2024), 959–984. arXiv:2210.15921
M. Choulli, Uniqueness of continuation for semilinear elliptic equations. Partial Differ. Equ. Appl. 5, 22 (2024). arXiv:2208.08378
M. Choulli, Hölder stability for a semilinear elliptic inverse problem. J. Math. Anal. Appl. 530 (2024) 127639. arXiv:2206.06746
M. Choulli, Stable determination of the nonlinear term in a quasilinear elliptic equation by boundary measurements. C. R. Math. Acad. Sci. Paris, 361 (2023), 1455-1470. arXiv:2205.16000
M. Choulli, Stability of determining the potential from partial boundary data in a Schrödinger equation in the high frequency limit. Communications on Analysis and Computation 1 (3) (2023) 214-233. arXiv:2307.00273
M. Bellassoued and M. Choulli, Global logarithmic stability of the Cauchy problem for anisotropic wave equations. Partial Differ. Equ. Appl. 4, 23 (2023). arXiv:1902.05878
M. Choulli, An inverse spectral problem for a fractional Schrödinger operator. Arch. Math. 120,395–402 (2023). arXiv:2211.12830
M. Choulli, Comments on the determination of the conductivity at the boundary from the Dirichlet-to-Neumann map. J. Math. Anal Appl. 517 (2) (2023), 126638. arXiv:2107.03061
M. Choulli, Correction to: A simple proof of a multidimensional Borg–Levinson type theorem. Semigroup Forum 104 (3) (2022) 766-772. arXiv1912.03055
E. Bonnetier, M. Choulli and F. Triki, Stability for quantitative photoacoustic tomography revisited. Res. Math. Sci 9, 24 (2022). arXiv 1905.07914
M. Bellassoued, M. Choulli, D. Dos Santos Ferreira, Y. Kian and P. Stefanov, A Borg-Levinson theorem for magnetic Schrödinger operators on a Riemannian manifold, Ann. Inst. Fourier 17 (6) (2021), 2471-2517. arXiv:1807.08857
M. Choulli, Some stability inequalities for hybrid inverse problems. C.R. Math. Acad. Sci. Paris 359 (10) (2021),1251-1265. arXiv:2012.09697
M. Choulli and M. Yamamoto, Gobal stability result for parabolic Cauchy problems. J. Inv. Ill-posed Problems 29 (6) (2021) 895-915. arXiv:1702.0629
M. Choulli, The property of unique continuation for second order evolution PDEs. Partial Differ. Equ. Appl. 2, 67 (2021). arXiv:2005.08475
M. Choulli, G. Hu, M. Yamamoto, Stability inequality for a semilinear elliptic inverse problem. Nonlinear Differ. Equ. Appl. 28, 37 (2021) 26 p. arXiv:2001.10940
M. Choulli, A simple proof of a multidimensional Borg-Levinson type theorem. Semigroup Forum, 102 (2) (2021), 575-582. arXiv:1912.03055
M. Choulli and G. Metafune, Two-sided Gaussian bounds for fundamental solutions of non-divergence form parabolic operators with Hölder continuous coefficients. Note Mat. 40 (2) (2020) 21-35. arXiv:1908.11054
K. Ammari, M. Choulli and F. Triki, A unified approach to solving some inverse problems for evolution equations by using observability inequalities. CSIAM Trans. Appl. Math. 1 (2020), 207-239. arXiv:1711.01779
M. Choulli, New global logarithmic stability result for the Cauchy problem for elliptic equations. Bull. Aust. Math. Soc. 101 (1) (2020) 141 -145. arXiv:1903.01136
K. Ammari, M. Choulli and L. Robbiano, Observability and stabilization of magnetic Schrödinger equations. J. Differential Equations 267 (2019) 3289-3327. arXiv:1711.05004
K. Ammari, M. Choulli and F. Triki, Hölder stability in determining the potential and the damping coefficient in a wave equation. J. Evol. Equ. 19 (2019), 305-319. arXiv:1609.06102
M. Choulli and F. Triki, Hölder stability for an inverse medium problem with internal data. Res. Math. Sci. 6, 9 (2019). arXiv:1712.04636
M. Choulli, Y. Kian and E. Soccorsi, Stability result for elliptic inverse periodic coefficient problem by partial Dirichlet-to-Neumann map. J. Spectr. Theory 8 (2018) 733-768. arXiv:1601.05355
M. Choulli, Corrigendum: An inverse problem in corrosion detection: stability estimates, J. Inv. Ill-posed Problems 12 (4) (2004) 349-367. J. Inverse Ill-Posed Probl. 26 (2018) 453-457. arXiv:1703.09914
M. Choulli and Y. Kian, Logarithmic stability in determining the time-dependent zero order coefficient in a parabolic equation from a partial Dirichlet-to-Neumann map. Application to the determination of a nonlinear term. J. Math. Pures Appl. 114 (2018) 235-261. arXiv:1605.08672
K. Ammari and M. Choulli, Determining a boundary coefficient in a dissipative wave equation: uniqueness and directional Lipschitz stability. Semigroup Forum 95 (2017) 527-538. arXiv:1503.04528
M. Choulli, Y. Kian and E. Soccorsi, On the Calderòn problem in periodic cylindrical domain with partial Dirichlet and Neumann data. Math. Methods Appl. Sci. 40 (16) (2017) 5959-5974. arXiv:1601.05358
K. Ammari and M. Choulli, Logarithmic stability in determining a boundary coefficient in an ibvp for the wave equation. Dynamics of PDE 14 (1) (2017) 33-45. arXiv:1505.07248
M. Choulli and L. Kayser, A remark on the Gaussian lower bound for the Neumann heat kernel of the Laplace-Beltrami operator. Semigroup Forum 94 (2017) 71-79. arXiv:1503.04529
M. Choulli, Various stability estimates for the problem of determining an initial heat distribution from a single measurement. Riv. Mat. Univ. Parma 7 (2) (2016) 279-307. arXiv:1512:07421
M. Choulli and E. Zuazua, Lipschitz dependence of the coefficients on the resolvent and greedy approximation for scalar elliptic problems. C. R. Math. Acad. Sci. Paris, Ser I 354 (2016) 1174-1187. arXiv:1605.04123
K. Ammari, M. Choulli and F. Triki, Determining the potential in a wave equation without a geometric condition. Extension to the heat equation. Proc. Amer. Math. Soc. 144 (10) (2016) 4381-4392. arXiv:1509.09078
M. Choulli and A. Jbalia, The problem of detecting corrosion by electric measurements revisited. Discrete Contin. Dyn. Syst. Ser. S 9 (3) (2016) 643-650. arXiv:1309.5901
M. Choulli, Y. Kian and E. Soccorsi, Stable determination of time-dependent scalar potential from boundary measurements in a periodic quantum waveguide. SIAM J. Math. Anal. 47 (6) (2015) 4536-4558. arXiv:1306.6601
M. Choulli, L. Kayser and E. M. Ouhabaz, Comments on Gaussian upper bound for Neumann heat kernels. Bull. Aust. Math. Soc. 92 (2015) 429-439. arXiv:1502.06740
M. Choulli and L. Kayser, Gaussian lower bound for the Neumann Green function of a general parabolic operator. Positivity 19 (3) (2015) 625-646. arXiv:1301.2906
M. Choulli, Y. Kian and E. Soccorsi, Double logarithmic stability in the identification of a scalar potential by partial elliptic Dirichlet-to-Neumann map. Bulletin SUSU MMCS 8 (3) (2015) 78-94 (in memory of Alfredo Lorenzi). arXiv:1501.01625
K. Ammari and M. Choulli, Logarithmic stability in determining two coefficients in a dissipative wave equation. Extensions to clamped Euler-Bernoulli beam and heat equations. J. Diff. Equat. 259 (7) (2015) 3344-3365. arXiv:1403.3018
M. Choulli and E. Soccorsi, An inverse anisotropic conductivity problem induced by twisting a homogeneous cylindrical domain. J. Spectr. Theory 5 (2) (2015) 295-329. arXiv:1209.5662
M. Choulli and F. Triki, New stability estimates for the inverse medium problem with internal data. SIAM J. Math. Anal. 47 (3) (2015) 1778-1799. arXiv:1511.03091
M. Choulli, L. Kayser, Y. Kian and E. Soccorsi, Heat trace asymptotics and boundedness in the second order Sobolev space of isospectral potentials for the Dirichlet Laplacian. Asymptot. Anal. 92 (2015) 259-278. arXiv:1312.3170
M. Choulli, Local boundedness property for parabolic BVP's and the gaussian bound for their Green functions. Evol. Equ. Control Theory 4 (1) (2015) 61-67. arXiv:1309.5903
M. Choulli and Y. Kian, Stability of the determination of time-dependent coefficient in parabolic equations. Math. Control and Related Fields 3 (2) (2013) 143-160. arXiv:1202.5392
M. Bellassoued, M. Choulli and A. Jbalia, Stability of the determination of the surface impedance of an obstacle from the scattering amplitude. Math. Methods Appl. Sci. 36 (18) (2013) 2429-2448. arXiv:1201.2552
M. Choulli and P. Stefanov, Stability for the multi-dimensional Borg-Levinson theorem with partial spectral data. Commun. PDE 38 (3) (2013) 455-476. arXiv:1111.0231
M. Choulli, O. Yu Imanuvilov, J-P. Puel and M. Yamamoto, Inverse source problem for linearized Navier-Stockes equations with data in arbitrary sub-domain. Appl. Anal. 92 (10) (2013) 2127-2143.
M. Choulli and M. Yamamoto, Global existence and stability for an inverse coefficient problem for a semilinear parabolic equation. Arch. Math (Basel) 97 (6) (2011) 587-597.
M. Bellassoued, M. Choulli and M. Yamamoto, Stability estimate for a multidimensional inverse spectral problem with partial data. J. Math. Anal. Appl. 378 (1) (2011) 184-197.
M. Bellassoued and M. Choulli, Stability estimate for an inverse problem for the magnetic Schrödinger equation from the Dirichlet-to-Neumann map. J. Funct. Anal. 258 (1) (2010) 161-195.
M. Bellassoued, M. Choulli and M. Yamamoto, Stability estimate for an inverse wave equation and a multidimensional Borg-Levinson theorem. J. Diff. Equat. 247 (2) (2009) 465-494.
M. Bellassoued and M. Choulli, Logarithmic stability in the dynamical inverse problem for the Schrodinger equation by an arbitrary boundary observation. J. Math. Pures Appl. 91 (3) (2009) 233-255.
M. Choulli and M. Yamamoto, Uniqueness and stability in determining the heat radiative coefficient, the initial temperature and a boundary coefficient in a parabolic equation. Nonlinear Anal. TMA 69 (11) (2008) 3983-3998.
M. Bellassoued, J. Cheng and M. Choulli, Stability estimate for an inverse boundary coefficient problem in thermal imaging. J. Math Anal. Appl. 343 (2008) 328-336.
J. Cheng, M. Choulli and J. Lin, Stable determination of a boundary coefficient in an elliptic equation. Math. Models Methods Appl. Sci. 18 (1) (2008) 107-123.
M. Choulli, On the determination of an inhomogeneity in an elliptic equation. Appl. Anal. 85 (6-7) (2006) 693-699.
M. Choulli and M. Yamamoto, Some stability estimates in determining sources and coefficients. J. Inv. Ill-Posed Problems 14 (4) (2006) 355-373.
M. Choulli, E. M. Ouhabaz and M. Yamamoto, Stable determination of a semilinear term in a parabolic equation. Commun. Pure Appl. Anal. 5 (3) (2006) 447-462.
J. Cheng, M. Choulli and X. Yang, An iterative BEM for the inverse problem of detecting corrosion in a pipe. Numer. Math. J. Chinese Univ. 14 (3) (2005) 252-266.
M. Choulli, An inverse problem in corrosion detection : stability estimates. Inv. Ill-Posed Problems 12 (4) (2004), 349-367.
M. Choulli and M. Yamamoto, Conditional stability in determining a heat source. J. Inv. Ill-Posed Problems 12 (3) (2004), 233-243.
M. Choulli, Local stability estimate for an inverse conductivity problem. Inverse Problems 19 (2003), 895-907.
M. Choulli, Stability estimate for an inverse elliptic problem. J. Inv. Ill-Posed Problems 10 (6) (2002), 601-610.
M. Choulli, On the determination of an unknown boundary function in a parabolic equation. Inverse Problems, 15 (1999), 659-667.
M. Choulli, A. Henrot and M. Mokhtar-Kharroubi, Domain derivative of the leading eigenvalue of a model transport operator. Transport Theory and Stat. Phy. 28 (4) (1999) 403-418.
M. Choulli and M. Yamamoto, Generic well-posedness of a linear inverse parabolic problem with respect to diffusion parameters. J. Inv. Ill-Posed Problems 7 (3) (1999) 241-254.
M. Choulli and P. Stefanov, An inverse boundary value problem for the stationary transport equation. Osaka J. Math. 36 (1999) 87-104.
M. Choulli and A. Henrot, Use of domain derivative to prove symmetry results in partial differential equations. Math. Nachr. 192 (1998) 91-103.
Th. Chatelain and M. Choulli, Clarke generalized gradient for eigenvalues. Commun. Appl. Anal. 1 (4) (1997) 443-454.
M. Choulli and M. Yamamoto, An inverse parabolic problem with non zero initial condition. Inverse Problems 13 (1997) 19-27.
M. Choulli and P. Stefanov, Reconstruction of coefficients of the stationary transport equation from boundary measurements. Inverse Problems 12 (1996) L19-L23.
M. Choulli and M. Yamamoto, Generic well-posedness of an inverse parabolic problem - Hölder space approach. Inverse Problems 12 (1996) 195-205.
M. Choulli and P. Stefanov, Inverse scattering and inverse boundary value problems for linear Boltzmann equation. Commun. PDE. 21 (5-6) (1996) 763-785.
M. Choulli and P. Stefanov, Scattering inverse pour l'équation du transport et relations entre les opérateurs de scattering et d'albédo. C. R. Acad. Sc. Paris, Série I 320 (1995) 947-952.
M. Choulli and A. Zeghal, Laplace transform approach for an inverse problem. Transport Theory and Statistical Physics 24 (9) (1995) 1353-1367.
M. Choulli, An inverse problem for a semilinear parabolic equation. Inverse Problems 10 (1994) 1123-1132.
M. Choulli, Une conséquence d'une version n-dimensionnelle du théorème de Borg-Levinson. C. R. Acad. Sc. Paris, Série I 317 (1993) 551-553.
M. Choulli, Determination of spatially-dependent scattering function for overspecified boundary conditions. Transport Theory and Statistical Physics 22 (1) (1993) 97-107.
M. Choulli, Un résultat d'existence pour un problème inverse. C. R. Acad. Sc. Paris, Série I 316 (1993) 1041-1046.
M. Choulli and A. Zeghal, Un résultat d'unicité pour un problème inverse semi-linéaire. C. R. Acad. Sc. Paris, Série I 315 (1992) 1051-1053.
M. Choulli, R. Deville and A. Rhandi, A general mountain pass principle for non differentiable functionnals. Revista de Matematicas Aplicadas 13 (1992) 45-58.
M. Choulli, Un problème inverse pour l'équation du transport. C. R. Acad. Sc. Paris, Série I 314 (1992) 897-900.
M. Choulli, An abstract inverse problem. J. Appl. Math. Stoc. Ana. 4 (2) (1991) 117-128.
M. Choulli, An abstract inverse problem and application. J. Math. Anal. Appl. 160 (1) (1991) 190-202.
M. Choulli, Uniqueness result for an unknown coefficient in nonlinear diffusion problem. Quart. Appl. Math. 47 (3) (1989) 429-433.
M. Choulli, Identifiability for an unknown coefficient in nonlinear diffusion equation. Quart. Appl. Math. 47 (1) (1989) 9-16.
Book chapters
J. Cheng, M. Choulli and S. Lu, An inverse conductivity problem in multifrequency electric impedance tomography. Inverse Problems and related Topics, Springer Proceedings in Mathematics and Statictics, Springer, Singapore, 2020, 3-30. arXiv:1903.08376
M. Choulli, Y. Kian and E. Soccorsi, Determining the scalar potential in a periodic quantum waveguide from the DN map. New Prospects in Direct, Inverse and Control Problems for Evolution Equations, A. Favini, G. Fragnelli and R. M. Mininni (Eds), Springer-INdAM, Roma, 2014, 93-105.
J. Cheng, M. Choulli and X. Yang, An iterative BEM for the inverse problem of detecting corrosion in a pipe. Frontiers and Prospects of Contemporary Applied Mathematics, 1-17, Ser. Contemp. Appl. Math. CAM 6, Higher Ed. Press, Beijing, 2005.
M. Mokhtar-Kharroubi, Mathematical topics in neutron transport theory. New aspects. With a chapter by M. Choulli and P. Stefanov. Series on Advances in Mathematics for Applied Sciences, 46. World Scientific Publishing Co., Inc., River Edge, NJ, 1997.
Th. Chatelain, M. Choulli and A. Henrot, Some new ideas for a Schiffer's conjecture. Modelling and Optimization of Distributed Parameter Systems with Applications to Engineering, K. Malanowski, Z. Nahorski and M. Peszynska (Eds), Chapman and Hall, London, 1996, 90-97.
M. Choulli and R. Deville, Local weak solutions for a multivalued evolution equation. Elliptic and Parabolic Problems, C. Bandle, J. Bemelmans, M.Chipot, J. Saint Jean Paulin and I. Shafrir (Eds). Pitman Research Notes in Mathematics, Longman, 1995, 74-81.
M. Choulli, Determination of the inhomogeneous term in evolution equations. Inverse Problems in Mathematical Physics, L. Päivärinta and E. Somersalo (Eds), Springer-Verlag, 1993, 16-21.
Other publications
M. Choulli, Comments on the quatitative uniquness of continuation for evolution equations. arXiv:2403.09564
M. Choulli, F. Triki and Q. Xue, Quantitative uniqueness of continuation result related to Hopf's lemma. arXiv:2105.02588
M. Choulli, Boundary value problems for elliptic partial differential equations, graduate course. arXiv:1912.05497
M. Choulli, Inverse problems for Schrödinger equations with unbounded potentials, notes of the course given during AIP 2019 summer school. arXiv:1909.11133
M. Choulli,O. Yu. Imanuvilov and M. Yamamoto, Inverse source problem for the Navier-Stokes equations. UTMS 2006-3.
M. Choulli and M. Yamamoto, Stable identification of a semilinear term in a parabolic equation. LMAM 2004-01.
M. Choulli, Sur l'inégalité isopérimétrique pour le problème de la rigidité à la torsion. Publications Mathématiques de Besançon 15 (1995-97) 41-45.
M. Choulli, Quelques remarques sur la théorie spectrale inverse. Publications Mathématiques de Besançon 14 (1993-94) 6 p.
M. Choulli and R. Deville, Un théorème du passage du col pour applications non différentiables. Séminaire d'Initiation à l'Analyse de Paris 6 4 (1991-92) 7p.
M. Choulli and R. Deville, Propriétés géométriques des espaces de Banach et régularité pour certaines équations d'évolution. Publications Mathématiques de Besançon 13 (1991) 46p.
M. Choulli, An inverse problem for linear transport equation. Problèmes inverses, rencontre interdisciplinaire, 28 novembre - 3 décembre 1991, Montpellier, France, 7 p.
M. Choulli, Problème inverse associé à une équation de diffusion. Publications Mathématiques de Besançon 11 (1988-89) 6 p.