Florian
Méhats
Publications
Warning: this
list has not been updated since end of 2019.
I am actually on leave from the University of
Rennes 1 as Research Associate at Ravel
Technologies.
Submitted
for publication
► Nonlinear
instability of inhomogeneous steady states solutions
to the HMF Model (with M. Lemou and A. M. Luz). Preprint
► A
micro-macro method for a kinetic graphene model in
one-space dimension (with N. Crouseilles, S. Jin and M. Lemou). Preprint
Published
or accepted papers
2019
► Highly-oscillatory
problems with time-dependent vanishing frequency (with P.
Chartier, M. Lemou and G. Vilmart), to appear in SIAM J.
Numer. Anal. Preprint
► A
new class of uniformly accurate numerical schemes for
highly oscillatory evolution equations (with
P. Chartier, M. Lemou and G. Vilmart), to appear in
Found. Comput. Math. Preprint
► Uniformly
accurate methods for Vlasov equations with
non-homogeneous strong magnetic field (with P. Chartier, N. Crouseilles, M. Lemou and
X. Zhao), to appear
in Math. of Comp. Preprint
► Stable
ground states for the HMF-Poisson model (with M. Fontaine and M. Lemou), Annales de
l'Institut Henri Poincaré C, Analyse non linéaire 36
(2019), no. 1, 217-255. Preprint
► Uniformly
accurate time-splitting methods for the semiclassical
linear Schrödinger equation. (with P.
Chartier and L. Le Treust), to
appear in ESAIM: Mathematical Modelling and Numerical
Analysis. Preprint
2017
► Uniformly
accurate Particle-In-Cell method for the long time
two-dimensional Vlasov-Poisson equation with strong
magnetic field (with N.
Crouseilles, M. Lemou and X. Zhao), J. Comput. Phys.
346 (2017), 172-190. Preprint
► Averaging
of nonlinear Schrödinger equations with strong
magnetic confinement (with R. L.
Frank and C. Sparber), Commun. Math. Sci 15 (2017),
no. 7, 1933-1945. Preprint
► The
quantum Liouville-BGK equation and the moment problem (with O. Pinaud), J. Diff. Eq. 263 (2017), no. 7,
3737-3787. Preprint
► Convergence
of
multi-revolution composition time-splitting methods
for highly
oscillatory differential equations of Schrödinger
type (with P. Chartier, M. Thalhammer and
Y. Zhang), ESAIM:M2AN 51 (2017),
no. 5, 1859-1882. Preprint
► Uniformly
accurate numerical schemes for the nonlinear Dirac
equation in the nonrelativistic limit regime (with M. Lemou and X. Zhao), Commun. Math. Sci. 15 (2017), no.
4, 1107-1128. Preprint
► Uniformly
accurate forward semi-Lagrangian methods for highly
oscillatory Vlasov-Poisson equations (with N. Crouseilles, M. Lemou
and X. Zhao), SIAM Multiscale Model. Simul. 15 (2017), no.
2, 723-744. Preprint
► Dimension
reduction for dipolar Bose-Einstein condensates in
the strong interaction regime (with W.
Bao and L. Le Treust), Kinetic and
Related Models, 10 (2017), no.3, 553-571. Preprint
► Nonlinear
stability criteria for the HMF model (with M. Lemou and A. M. Luz),
Arch. Rational Mech. Anal. 224 (2017), no. 2, 353-380. Preprint
► Highly-oscillatory
evolution equations with multiple frequencies:
averaging and numerics (with
P. Chartier and M. Lemou), Numer. Math. 136 (2017),
no. 4, 907-939. Preprint
2016
► Dimension
reduction for rotating Bose-Einstein condensate with
anisotropic confinement (with
C. Sparber),
DCDS-A 36 (2016), no. 9, 5097-5118. Preprint
► A
kinetic model for the transport of electrons in a
graphen layer
(with C. Fermanian
Kammerer), J. Comp. Phys. 327 (2016), 450-483.
Preprint
► Strong
confinement limit for the nonlinear Schrödinger
equation constrained on a curve (with N. Raymond)
to appear in Ann. Henri Poincaré. Preprint
► Improved
error estimates for splitting methods applied to
highly-oscillatory nonlinear Schrödinger equations (with P. Chartier, M. Thalhammer and
Y. Zhang), Math. of Comp.
85 (2016), 2863-2885.
Preprint
► The
Interaction
Picture method for solving the
generalized nonlinear Schrödinger equation in optics (with S. Balac, A. Fernandez,
F. Mahé and R.
Texier-Picard), M2AN Math. Model. Numer. Anal. 50 (2016)
945-964. Preprint
► Solving highly-oscillatory
NLS with SAM: numerical efficiency and long-time
behavior
(with P. Chartier, N. Mauser and Y.
Zhang),
to appear in DCDS-S. Preprint
2015
► Models
of dark matter halos based on statistical mechanics:
II. The fermionic King model (with P.-H. Chavanis and M.
Lemou),
Phys. Rev. D 92 (2015), 123527. Preprint
► Models
of dark matter halos based on statistical mechanics:
I. The classical King model (with P.-H. Chavanis and M.
Lemou),
Phys. Rev. D 91 (2015), 063531. Preprint
► Dimension
reduction for anisotropic Bose-Einstein condensates
in the strong interaction regime (with W.
Bao and L. Le Treust),
Nonlinearity 28 (2015), no. 3, 755. Preprint
► Stroboscopic
averaging
for the nonlinear Schrödinger equation (with F. Castella, P. Chartier
and A. Murua), Found. Comput. Math 15
(2015), no. 2, 519–559. Preprint
► Numerical
study of a quantum-diffusive
spin model for two-dimensional electron gases
(with L. Barletti, C. Negulescu and S.
Possanner), Comm. Math. Sci. 13, (2015),
1347--1378. Preprint
► Uniformly
accurate numerical
schemes for highly oscillatory Klein-Gordon and
nonlinear Schrödinger
equations
(with P. Chartier, N.
Crouseilles and M. Lemou),
Numer. Math. 129 (2015), no. 2, 211-250. Preprint
2014
► On the
controllability of quantum transport in an
electronic nanostructure (with Y. Privat and M.
Sigalotti),
SIAM J. Appl. Math, 74 (2014), no. 6, 1870–1894. Preprint
► Analysis
of models for quantum transport of electrons in
graphene layers (with R. El
Hajj), Math. Models Methods
Appl. Sci. 24, (2014), no. 11, 2287-2310. Preprint
2013
► An
asymptotic
preserving scheme based on a new formulation for
NLS in the
semiclassical limit (with C.
Besse and R. Carles),
SIAM Multiscale Model. Simul. 11 (2013), no. 4,
1228-1260. Preprint
► Asymptotic
preserving
schemes for highly oscillatory
Vlasov-Poisson equations (with
N. Crouseilles and M. Lemou), J. Comp. Phys.
248 (2013) 287–308. Preprint
2012
► Micro-macro
schemes for
kinetic equations including
boundary layers (with M. Lemou),
SIAM J. Sci.
Comp. 34 (2012), no. 6, 134–760. Preprint
► Stable
ground states and
self-similar blow-up
solutions for the gravitational Vlasov-Manev system (with M. Lemou and C. Rigault),
SIAM J. Math.
Anal. 44 (2012), no. 6, 3928-3968. Preprint
► Orbital
stability
of spherical galactic models (with
M. Lemou and P. Raphaël),
Inventiones Math. 187
(2012) 145–194. Preprint
2011
► 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
► A
problem of moment
realizability in quantum statistical physics
(with O. Pinaud), Kinet. Relat.
Models, 4
(2011), no. 4, 1143-1158. 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
► The
Schrödinger Poisson
system on the sphere (with P.
Gérard), SIAM J. Math. Anal. 43 (2011), no.3,
1232–1268. 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
2010
► An
inverse problem
in quantum statistical physics (with
O. Pinaud), J. Stat. Phys. 140
(2010), no. 3, 565–602.
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
► 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
2009
► 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.
► 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
► 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
► 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
2008
► 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
► 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
► 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
►
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
2007
► On
Quantum
Hydrodynamic and Quantum Energy Transport Models (with P. Degond & S.
Gallego), Commun. Math. Sci. 5 (2007), no. 4,
887-908. 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
► 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
► 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
2006
► 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.
► 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
► 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
► Analysis
of
a quantum subband model for the transport of
partially confined
charged particles,
Monatsh.
Math. 147 (2006), 43-73. 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
2005
► Entropic
discretization of a quantum
drift-diffusion model (with S. Gallego), SIAM J.
Numer. Anal. 43 (2005), no. 5, 1828-1849. 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
► 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
► 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
► On
an
open transient Schrödinger-Poisson system (with
N.
Ben Abdallah & O. Pinaud), Math. Models Methods
Appl. Sci. 15 (2005),
667--688. 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
► 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
2004
► On a
Vlasov-Schrödinger-Poisson model (with N. Ben
Abdallah), Comm.
Partial Differential Equations 29 (2004), no.
1-2,
173-206.
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
► Numerical
approximation
of a quantum drift-diffusion model (with
S.
Gallego), C. R.
Acad. Sci. Paris, Ser.
I 339 (2004), 519-524.
Preprint
2002
► 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
► 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
2001
► On
singular
perturbation problems for the
nonlinear Poisson equation (with A. Ambroso
& P.-A.
Raviart), Asymptot. Anal. 25 (2001), no. 1,
39-91.
Preprint
1999
► 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
► The
Child-Langmuir
asymptotics for magnetized flows (with N. Ben
Abdallah & P. Degond), Asymptot. Anal. 20 (1999),
no. 2,
97-132.
Preprint
1998
► 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
1995
► 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.
PhD
thesis and Habilitation thesis
► Etude
mathématique et analyse asymptotique de modèles
quantiques : transport, confinement et
collisions,
HDR soutenue le 23 novembre 2004 à l'Université
Toulouse 3.
► Etudes
de
problèmes aux limites en Physique du Transport
des
Particules Chargées, Thèse
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.
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