Accueil Publications Curriculum Vitae Enseignement Liens

 

Florian Méhats

Publications classified by subject (for the same list of publications in reverse chronological order, click here)

 

Numerical methods for stiff problem

► Micro-macro schemes for kinetic equations including boundary layers (with M. Lemou). Preprint

► A boundary matching  micro/macro decomposition for kinetic equations (with M. Lemou), C. R. Acad. Sci. Paris, Ser. I 349 (2011) 479–484.. Preprint

► An asymptotic preserving scheme for the Schrödinger equation in the semiclassical limit (with P. Degond & S. Gallego), C. R. Math. Acad. Sci. Paris 345 (2007), no. 9, 531--536. Preprint

 

Gravitation models

► Stable ground states and self-similar blow-up solutions for the gravitational Vlasov-Manev system (with M. Lemou and C. Rigault). Preprint

► Orbital stability of spherical galactic models (with M. Lemou and P. Raphaël), arXiv:1007.4095, to appear in Inventiones Math. Preprint

► Stable ground states for the gravitational Vlasov-Manev system (with M. Lemou and C. Rigault). Preprint

► A new variational approach to the stability of gravitational systems (with M. Lemou and P. Raphaël), Comm. Math. Phys. 302 (2011), 161–224. Preprint

► Evaporation law in kinetic gravitational systems described by simplified Landau models (with P. Carcaud, P.-H. Chavanis and M. Lemou), , Discrete Contin. Dyn. Syst. B 14 (2010), no. 3, 907–934.  Preprint

► A new variational approach to the stability of gravitational systems (with M. Lemou and P. Raphaël), C. R. Math. Acad. Sci. Paris 347  (2009),  no. 15--16, 979--984.

► Stable ground states for the relativistic gravitational Vlasov-Poisson system (with M. Lemou and P. Raphaël), Comm. Partial Diff. Eq. 34 (2009), no. 7, 703-721. Preprint

► Stable self-similar blow up dynamics for the three dimensional relativistic gravitational Vlasov-Poisson system (with M. Lemou and P. Raphaël), J. Amer. Math. Soc. 21 (2008), 1019-1063. Preprint

► Structure of the linearized gravitational Vlasov-Poisson system close to a polytropic ground state (with M. Lemou and P. Raphaël), SIAM J. Math. Anal. 39 (2008), no. 6, 1711-1739. Preprint

► Uniqueness of the critical mass blow up solution for the four dimensional gravitational Vlasov-Poisson system (with M. Lemou and P. Raphaël), Ann. I. H. Poincaré - AN 24 (2007) 825--833. Preprint

► On the orbital stability of the ground states and the singularity formation for the gravitational Vlasov Poisson system (with M. Lemou & P. Raphaël), Arch. Ration. Mech. Anal. 189 (2008), no. 3, 425-468. Preprint

► On the orbital stability of the ground states and the singularity formation for the gravitational Vlasov Poisson system (with M. Lemou and P. Raphaël), C. R. Math. Acad. Sci. Paris 341 (2005), no. 4, 269-274. Preprint

 

Strong partial confinement for Schrödinger-Poisson or NLS

► Second order averaging for the nonlinear Schrödinger equation with strong anisotropic potential (with N. Ben Abdallah, Y. Cai and F. Castella), Kinet. Relat. Models, 4 (2011), no. 4, 831-856. Preprint

► The Schrödinger Poisson system on the sphere (with P. Gérard), SIAM J. Math. Anal. 43 (2011), no.3, 1232–1268. Preprint 

► An effective mass theorem for the bidimensional electron gas in a strong magnetic field (with F. Delebecque-Fendt), Comm. Math. Phys. 292 (2009), no. 3, 829-870. Preprint

► The strongly confined Schrödinger-Poisson system for the transport of electrons in a nanowire (with N. Ben Abdallah, F. Castella and F. Delebecque-Fendt), SIAM J. Appl. Math. 69 (2009), no. 4, 1162-1173. Preprint

► Time averaging for the strongly confined nonlinear Schrödinger equation, using almost periodicity (with N. Ben Abdallah and F. Castella), J. Diff. Eq. 245, (2008), no 1, 154-200. Preprint

► The nonlinear Schrödinger equation with strong anisotropic harmonic potential (with N. Ben Abdallah, C. Schmeiser & R. M. Weishäupl), SIAM J. Math. Anal., 37 (2005), no. 1, 189-199. Preprint

► Analysis of a quantum subband model for the transport of partially confined charged particles,  Monatsh. Math. 147 (2006), 43-73. Preprint

► Adiabatic approximation of the Schrödinger-Poisson system with a partial confinement (with N. Ben Abdallah & O. Pinaud), SIAM J. Math. Anal. 36 (2005), no. 3, 986-1013. Preprint

 

Quantum hydrodynamics, quantum drift-diffusion

► A problem of moment realizability in quantum statistical physics (with O. Pinaud), Kinet. Relat. Models, 4 (2011), no. 4, 1143-1158. Preprint

► An inverse problem in quantum statistical physics (with O. Pinaud), J. Stat. Phys. 140 (2010), no. 3, 565--602. Preprint

► Quantum drift-diffusion modeling of spin transport in nanostructures (with L. Barletti), J. Math. Phys. 51 (2010), 053304. Preprint

► Derivation of viscous correction terms for the isothermal quantum Euler model (with S. Brull), Z. Angew. Math. Mech. 90 (2010), no. 3, 219 – 230. Preprint

► On Quantum Hydrodynamic and Quantum Energy Transport Models (with P. Degond & S. Gallego), Commun. Math. Sci. 5 (2007), no. 4, 887-908. Preprint

► Quantum hydrodynamic and diffusion models derived from the entropy principle (with P. Degond, S. Gallego and C. Ringhofer), lecture notes of a course by P. Degond at Cetraro, september 2006.

► Isothermal quantum hydrodynamics: derivation, asymptotic analysis and simulation (with P. Degond & S. Gallego), SIAM Multiscale Model. Simul.  6 (2007), no. 1, 246-272. Preprint

► An entropic Quantum Drift-Diffusion model for electron transport in resonant tunneling diodes (with P. Degond & S. Gallego), J. Comput. Phys. 221 (2007), 226-249. Preprint

► On quantum extensions to classical Spherical Harmonics Expansion / Fokker-Planck models (with J.-P. Bourgade, P. Degond & C. Ringhofer), J. Math. Phys. 47 (2006), no. 4, 043302. Preprint

► Entropic discretization of a quantum drift-diffusion model (with S. Gallego), SIAM J. Numer. Anal. 43 (2005), no. 5, 1828-1849. Preprint

► Numerical approximation of a quantum drift-diffusion model (with S. Gallego), C. R. Acad. Sci. Paris, Ser. I 339 (2004), 519-524. Preprint

► Quantum Energy-Transport and Drift-Diffusion models (with P. Degond & C. Ringhofer), J. Stat. Phys. 118 (2005), no. 3-4, 625-665. Preprint

► Quantum hydrodynamic model derived from the entropy principle (with P. Degond & C. Ringhofer), Contemp. Math. 371 (2005), 107-131. Preprint

 

Hybrid classical-quantum models : subband models

► Adiabatic quantum fluid transport models (with N. Ben Abdallah & C. Negulescu), Comm. Math. Sci.  4 (2006), no. 3, 621--650. Preprint

► Diffusive transport of partially quantized particles: Existence, uniqueness and long time behaviour (with N. Ben Abdallah and N. Vauchelet), Proc. of the Edinburgh Math. Soc. 49 (2006), 513--549. Preprint

► Global existence of classical solutions for a Vlasov-Schrödinger-Poisson system (with N. Ben Abdallah & G. Quinio), Indiana Univ. Math. J. 55 (2006), no. 4, 1423--1448. Preprint

► Semiclassical Analysis of the Schrödinger equation with a partially confining potential (with N. Ben Abdallah), J. Math. Pures Appl. 84 (2005), 580-614. Preprint

► A note on the long time behavior for the Drift-Diffusion-Poisson system  (with N. Ben Abdallah & N. Vauchelet), C. R. Acad. Sci. Paris, Ser. I 339 (2004), 683-688. Preprint

► On a Vlasov-Schrödinger-Poisson model (with N. Ben Abdallah), Comm. Partial Differential Equations 29 (2004), no. 1-2, 173-206. Preprint

► Analysis of a Drift-Diffusion-Schrödinger-Poisson model (with N. Ben Abdallah & N. Vauchelet), C. R. Acad. Sci. Paris Sér. I  335 (2002), 1007-1012. Preprint

 

Open quantum systems and other topics related to Schrödinger

► An asymptotic preserving scheme for the Schrödinger equation in the semiclassical limit (with P. Degond & S. Gallego), C. R. Math. Acad. Sci. Paris 345 (2007), no. 9, 531--536. Preprint

► On an open transient Schrödinger-Poisson system (with N. Ben Abdallah & O. Pinaud), Math. Models Methods Appl. Sci. 15 (2005), 667--688. Preprint

 

Plasma models

► On singular perturbation problems for the nonlinear Poisson equation (with A. Ambroso & P.-A. Raviart), Asymptot. Anal. 25 (2001), no. 1, 39-91. Preprint

► The Child-Langmuir asymptotics for magnetized flows (with N. Ben Abdallah & P. Degond), Asymptot. Anal. 20 (1999), no. 2, 97-132. Preprint

► Mathematical models for magnetic insulation (with N. Ben Abdallah & P. Degond), Phys. Plasmas 5 (1998), no. 5, 1522-1534. Preprint

► The Child-Langmuir asymptotics applied to a bipolar diode, Math. Methods Appl. Sci. 21 (1998), no. 12, 1115-1148. Preprint

 

An oblique derivative boundary value problem

► Convergence of a numerical scheme for a nonlinear oblique derivative boundary value problem, M2AN: Math. Model Numer. Anal. 36 (2002), no. 6, 1111--1132. Preprint

► A nonlinear oblique derivative boundary value problem for the heat equation. Part 2: Singular selfsimilar solutions (with J.-M. Roquejoffre), Ann. Inst. H. Poincaré Anal. Non Linéaire 16 (1999), no. 6, 691-724. Preprint

► A nonlinear oblique derivative boundary value problem for the heat equation. Part 1: Basic results (with J.-M. Roquejoffre), Ann. Inst. H. Poincaré Anal. Non Linéaire 16 (1999), no. 2, 221-253. Preprint

► Un problème d'évolution avec condition aux limites non linéaire (with J.-M. Roquejoffre), C. R. Acad. Sci. Paris Sér. I Math. 321 (1995), no. 10, 1319-1322.

 

Habilitation à diriger des recherches et Thèse de doctorat

► Etude mathématique et analyse asymptotique de modèles quantiques : transport, confinement et collisions, soutenue le 23 novembre 2004 à l'Université Toulouse 3.

► Etudes de problèmes aux limites en Physique du Transport des Particules Chargées, soutenue le 9 décembre 1997 à l'Ecole polytechnique.

 

Proceedings

► A Drift-Diffusion subband model for the double-gate MOSFET (with N. Ben Abdallah, P. Pietra & N. Vauchelet), 5th IEEE Conference on Nanotechnology, Nagoya, July 11-15, 2005.

► Numerical discretization of a fully Quantum Drift-Diffusion model (with P. Degond & S. Gallego), Computational Fluid and Solid Mechanics 2005, K. J. Bathe Ed., Elsevier. Proceedings Third MIT Conference on Fluid and Solid Mechanics, June 14-17, 2005.

► Simulation of 2D quantum transport in ultrashort DG-MOSFETs : a fast algorithm using subbands (with N. Ben Abdallah, E. Polizzi, M. Mouis), Simulation of Semiconductor Processes and Devices, 2003. SISPAD 2003. International Conference on 3-5 Sept. 2003, 267-270.