Mes travaux de recherche portent sur l’étude mathématique et la simulation numérique des problèmes directs ou inverses (notamment pour les ondes), ainsi que sur le contrôle et la stabilisation des EDP. La liste complète des mes travaux est disponible ci-dessous.

Articles

• Observer-based feedback-control for the stabilization of a class of parabolic systems. Imene Djebour, Karim Ramdani, Julie Valein. Submitted.

• Homogenization of a transmission problem with sign-changing coefficients and interfacial flux jump. R. Bunoiu, K. Ramdani, C Timofte. Communications in Mathematical Sciences, 21 (7), (2023), 2029-2049.

• A reconstruction method for the inverse gravimetric problem. Anthony Gerber-Roth, Alexandre Munnier, Karim Ramdani. SMAI Journal of Computational Mathematics, 9, (2023), 197-225.

• T-coercivity for the homogenization of sign-changing coefficients scalar problems with extreme contrasts. R. Bunoiu, K. Ramdani, C Timofte. Mathematical Reports, 24 (74), (2022), 113-123.

• T-coercivity for the asymptotic analysis of scalar problems with sign-changing coefficients in thin periodic domains. R. Bunoiu, K. Ramdani, C Timofte. Electronic Journal of Differential Equations, 2021(6), (2021), 1-22.

• Homogenization of Maxwell’s equations and related scalar problems with sign-changing coefficients. R. Bunoiu, L. Chesnel, K. Ramdani, M. Rihani. Annales de la Faculté des Sciences de Toulouse : Mathématiques, Ser. 6, 30 (5), (2021), 1075-1119.

• Calderón cavities inverse problem as a shape-from-moments problem. A. Munnier, K. Ramdani. Quart. Appl. Math., 76, (2018), 407-435.

• Adaptive observer for age-structured population with spatial diffusion. K. Ramdani, J. Valein, J.-C. Vivalda. North-W. Eur. J. of Math., 4, (2018), 39-58.

• Conformal mapping for cavity inverse problem: an explicit reconstruction formula. A. Munnier, K. Ramdani. Applicable Analysis, 96 (1), (2017), 108-129.

• Detectability and state estimation for linear age-structured population diffusion models. K. Ramdani, M. Tucsnak, J. Valein. M2AN, 50 (6), (2016), 1731-1761.

• Homogenization of materials with sign changing coefficients. R. Bunoiu, K. Ramdani. Communications in Mathematical Sciences, 14 (4), (2016), 1137-1154.

• On the detection of small moving disks in a fluid. A. Munnier, K. Ramdani. SIAM J. Appl. Math., 76 (1), (2016), 159-177.

• Asymptotic analysis of a Neumann problem in a domain with cusp. Application to the collision problem of rigid bodies in a perfect fluid. A. Munnier, K. Ramdani. SIAM J. Math. Anal., 47 (6), (2015), 4360-4403.

• Reconstructing the potential for the 1D Schrödinger equation from boundary measurements. S. Avdonin, V. Mikhaylov, K. Ramdani. IMA J. Math. Control Inform.,  31 (1), (2014), 137-150.

• Far field model for time reversal and application to selective focusing on small dielectric inhomogeneities. C. Burkard, A. Minut, K. Ramdani. Inverse Problems and Imaging, 7 (2), (2013), 445-470.

• Transparent boundary conditions for locally perturbed infinite hexagonals periodic media. C. Besse, J. Coatléven, S. Fliss, I. Violet-Lacroix, K. Ramdani. Communications in Mathematical Sciences, 11 (4), (2013), 907-938.

• Wide frequency band numerical approaches for multiple scattering problems by disks. X. Antoine, K. Ramdani, B. Thierry. J. Algorithms Comput. Technol., 6 (2), (2012), 241-259.

• Reconstructing initial data using observers : error analysis of the semi-discretes and fully discrete approximations. G. Haine, K. Ramdani. Numer. Math., 120 (2), (2012), 307-343.

• Observateurs itératifs en horizon fini. Application à la reconstruction de données initiales pour des EDP d’évolution. G. Haine, K. Ramdani. Journal Européen des Systèmes Automatisés (JESA), 45, (2011), 715-724.

• A time reversal based algorithm for solving initial data inverse problems. K. Ito, K. Ramdani, M. Tucsnak. Discrete Contin. Dyn. Syst. Ser. S, 4 (3), (2011), 641-652.

• Recovering the initial state of an infinite-dimensional system using observers. K. Ramdani, M. Tucsnak, G. Weiss. Automatica, 46 (10), (2010), 1616-1625.

• A construction of beam propagation methods for optical waveguides. X. Antoine, P. Dreyfuss, K. Ramdani. Commun. Comput. Phys., 6 (3), (2009), 565-576.

• Far field modelling of electromagnetic time-reversal and application to selective focusing on small scatterers. X. Antoine, B. Pinçon, K. Ramdani, B. Thierry. SIAM J. Appl. Math., 69 (3), (2008), 830-844.

• Transmission through a thick periodic slab. S. Shipman, K. Ramdani. M3AS, 18 (4), (2008), 543-572.

• On the numerical approximation of high-frequency acoustic multiple scattering problems by circular cylinders. X. Antoine, C. Chniti, K. Ramdani. J. Comp. Phy., 227, (2008), 1754-1771.

• Numerical simulation of acoustic time reversal mirrors. C. Ben Amar, N. Gmati, C. Hazard, K. Ramdani. SIAM J. Appl. Math., 67(3), (2007), 777-791.

• Selective focusing on small scatterers in acoustic waveguides using time reversal mirrors. B. Pinçon, K. Ramdani. Inverse Problems, 23 (1), (2007), 1-25.

• Uniformly exponentially stable approximations for a class of second order evolution equations. Application to LQR optimization problems. K. Ramdani, T. Takahashi, M. Tucsnak. ESAIM Control Optim. Calc. Var., 13 (3), (2007), 503-527.

• Semi-discrétisation en espace du problème de la stabilisation interne de l’équation des poutres. K. Ramdani, T. Takahashi, M. Tucsnak. ESAIM Proceedings, 18, (2007), 48-59.

• Internal stabilization of the plate equation in a square : the continuous and the semi-discretized problems. K. Ramdani, T. Takahashi, M. Tucsnak. J. Math. Pures Appl., 85 (1), (2006), 17-37.

• A spectral approach for the exact observability of infinite dimensional systems with skew-adjoint generator. K. Ramdani, T. Takahashi, G. Tenenbaum, M. Tucsnak. J. Funct. Anal, 226 (1), (2005), 193-229.

• Selective acoustic focusing using time-harmonic reversal mirrors. C. Hazard, K. Ramdani. SIAM J. Appl. Math., 64 (3), (2004), 1057-1076.

• A non elliptic spectral problem related to the analysis of superconducting transmission lines. A-S. Bonnet-Bendhia, K. Ramdani. M2AN, 39 (2), (2002), 461-487.

• Diffraction by an acoustic grating perturbed by a bounded obstacle. A-S. Bonnet-Bendhia, K. Ramdani. Adv. Comp. Math., 16 (2/3), (2002), 113-138.

• A constraint on the maximum reflectance of rapidly oscillating dielectric. G. Bao, D. Dobson, K. Ramdani. SIAM J. Contr. Opt., 40 (6), (2002), 1858-1866.

• Diffraction par un obstacle situé dans un réseau de plaques semi-infinies. A-S. Bonnet-Bendhia, K. Ramdani, A. Tillequin. C. R. Acad. Sci. Paris Série I Math., 331 (2000), 977-982.

• Mathematical analysis of conducting and superconducting transmission lines. A-S. Bonnet-Bendhia, K. Ramdani. SIAM J. Appl. Math, 60 (6), (2000), 2087-2113.

• Analyse spectrale et singularités d’un problème de transmission non coercif. A-S. Bonnet-Bendhia, M. Dauge, K. Ramdani. C. R. Acad. Sci. Paris Série I Math., 328 (1999), 717-720.

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Chapitre de livre

Computational Methods for Multiple Scattering at High Frequency with Applications to Periodic Structures Calculations. X.Antoine, C. Geuzaine, K. Ramdani. Wave Propagation in Periodic Media – Analysis, Numerical Techniques and Practical Applications, Edit.: M. Ehrhardt, Progress in Computational Physics, Vol. 1, Bentham Science Publishers Ltd., (2010), 73-107.

HDR (Université Nancy 1, 19 Octobre 2007)

Guider, piéger, focaliser et contrôler les ondes. Une contribution mathématique et numérique.

Jury : Xavier ANTOINE, Claude BARDOS (Président), Anne-Sophie BONNET-BENDHIA, François CASTELLA, Gilles LEBEAU (Rapporteur), Antoine HENROT, Marius TUCSNAK, Enrique ZUAZUA (Rapporteur)   

Thèse (Université Paris 6, 7 janvier 1999)

Lignes supraconductrices : analyses mathématique et numérique.

Jury : Mikhaël BALABANE (Président), Henri BAUDRAND, Yann BRENIER, Anne-Sophie BONNET-BENDHIA (Directrice), Gabriel CALOZ, Patrick JOLY, Alexander KOMECH, Marc LENOIR