Publications
Sur l' équation
de Boltzmann homogène et sa relation avec l'équation de
Landau-Fokker-Planck : influence des collisions rasantes ,
CRAS, 324, 265-270, 1997.
Existence of
solutions of transport equations with non linear boundary conditions ,
European J. Mech. B/Fluids, 16, 557-574, 1997.
Generalized
invariant sets for the Boltzmann equation ,
Math. Mod. Meth.
Appl. Math., 7, 457-476, 1997.
On
Boltzmann equations and Fokker-Planck asymptotics : influence of grazing
collisions ,
J. Stat. Phys., 89, 151-176, 1997.
Generalized
Maxwell boundary conditions for transport equations,
preprint.
On a
Fokker-Planck equation arising in population dynamics
,
with M.
SAAD (MAB, Universite Bordeaux 1),
Revista Matematica Compl., 11, 2, 353-372, 1998.
Zero-electron-mass limits in hydrodynamic models for plasmas ,
with A. JUNGEL (TU Berlin)
and Y. J. PENG (Univ. Clermont-Ferrand), Applied Math. Letters, 12, 75-79,
1999.
Vanishing
pressure in gas dynamic equations ,
with S. JUNCA (Labo. Dieudonné et IUFM, Nice),
ZAMP, Vol. 51/1 143-148, 2000.
Approximation by
homogeneization and diffusion of kinetic equations ,
with
F. POUPAUD (Labo. Dieudonné, Nice), Comm. PDE., 26, 537-569, 2001.
Lifshitz-Slyozov
equations: the model with encounters ,
with J.-F. COLLET
(Labo. Dieudonné, Nice), TTSP, 28, n. 6, 545-573, 1999.
Parabolic
equations involving 0th and 1st order terms with L1 data ,
with
M. SAAD (MAB, Université Bordeaux 1),
Revista Matematica Iberoamericana,
17, 433-470, 2001.
On solutions of the
Lifshitz-Slyozov model,
with J.F. COLLET (Labo. Dieudonné,
Nice), Nonlinearity, 13, 1239-1262, 2000.
Solutions d'équilibre
pour l'opérateur de Pauli,
CRAS, 330, 1035-1038,
2000.
Diffusion limit for non
homogeneous and non microreversible processes ,
with F. POUPAUD (Labo. Dieudonn é, Nice) and P. DEGOND (Toulouse),
Indiana Univ. Math. J., 49, 1175-1198, 2000.
Fourier-based metrics and
Berry-Esseen like inequalities ,
with G. TOSCANI (Univ. Pavia)
and S. JUNCA (Labo. Dieudonné, Nice),
Monatshefte f\"ur Mathematik, 135,
115-136 (2002).
Asymptotic problems
for a kinetic model of two-phase flow,,
Proc. Royal Soc. Edimburgh., 131, 1371-1384, 2001.
Diffusion
approximation in heterogeneous media,,
with A. MELLET
(Toulouse),
Asymptotic Analysis, 28, 331-358, 2001.
The Becker-Doring system and its Lifshitz-Slyozov limit,,
with
J.F. COLLET, F. POUPAUD and A. VASSEUR (Labo. J. A. Dieudonné,
Nice),
SIAM J. Appl. Math., 62, 1488-1500, 2002.
Some mathematical results on the kinetic theory of phase transitions,
with J.F. COLLET, S. HARIZ, F. POUPAUD and A. VASSEUR (Labo. J. A.
Dieudonné, Nice),
in
Transport in Transition Regimes, IMA Volumes in Mathematics and its Applications,
Edited by N. Ben Abdallah, A. Arnold, P. Degond,
I. Gamba, R. Glassey, D. Levermore, and C. Ringhofer,
pp. 103--120.
Some remarks on
large-time asymptotics of the Lifshitz-Slyozov equations,
with J.F. COLLET and A. VASSEUR (Labo. J. A. Dieudonné, Nice)
J. Stat. Phys., 108, 341-359, 2002.
Numerical
investigation of the behaviour of solutions of the Lifshitz-Slyozov
equations
, with J.A. CARRILLO (Univ.
Granada),
Rapport de recherche INRIA, RR-4287, 2001;
J. Sci. Comp., 20, 1,69-113, 2004.
Discrete version of
the SHE asymptotics: multigroup neutron equations,
with A.
MELLET (Toulouse),
Rapport de recherche INRIA, RR-4302, 2001;
J. Math. Phys., 43, 6, 3232-3260, 2002.
Analysis of a
semi-discrete version of the Wigner equation,
SIAM J. Num. Anal., 40, 6, 2007-2025, 2002.
Equilibration rate for
the linear inhomogeneous relaxation-time Boltzmann equation for charged
particles,
with M. J. CACERES, J. A. CARRILLO
(Granada)
Comm. PDE., 28, 969-989, 2003.
On fluid limit for the
semiconductors Boltzmann equation ,
with A. MELLET
(Toulouse)
J. Diff. Eq., 189, 17-45, 2003.
Homogenization and
diffusion asymptotics for the linear Boltzmann equation,
with A.
MELLET (Toulouse),
ESAIM-COCV, 9, 371-398, 2003.
Homogenization of
transport equations: weak mean field approximation,
with F.
POUPAUD (Nice),
SIAM J. on Mathematical Analysis, 36, 3, 856 - 881, 2004.
Low-field limit for a
nonlinear discrete drift-diffusion model arising in semiconductor
superlattices theory,
with L. BONILLA (Madrid), O. SANCHEZ, J. SOLER (Granada),
SIAM J. Appl. Math., 64, 1526 - 1549, 2004.
Hydrodynamic limits
for the Vlasov-Navier-Stokes equations. Part I: Light particles regime ,
with
P.-E. JABIN (ENS), A. VASSEUR (Nice),
Indiana University Math. J., 53, 1495--1516, 2004.
Hydrodynamic limits
for the Vlasov-Navier-Stokes equations. Part II: Fine particles regime
,
with P.-E. JABIN (ENS), A. VASSEUR (Nice),
Indiana University Math. J., 53, 1517-1536, 2004.
Multidimensional high field limit of the electrostatic
Vlasov-Poisson-Fokker-Planck system
,
with J. J. NIETO (Granada), F. POUPAUD (Nice), J. SOLER (Granada)
J. Differential Eq., 213, no. 2, 418--442, 2005.
On the modeling of the
transport of particles in turbulent flows
with F. POUPAUD (Nice),
Mathematical Modelling and Numerical Analysis (M2AN), 38, 673--690, 2004.
Homogenization of transport equations: A simple PDE approach to the Kubo
formula
,
with F. POUPAUD (Nice)
Bulletin Sci. Math., 131, 72--88, 2007.
Hydrodynamic Limit for the Vlasov-Poisson-Fokker-Planck System:
Analysis of
the Two-Dimensional Case
,
Math. Mod. Meth. Appl. Sci. (M3AS), 15, no. 5, 737--752, 2005.
The strong relaxation limit of the multidimensional
isothermal Euler equations,
with J.-F. COULOMBEL (Lille), Preprint, to appear in Trans. AMS.
A coupled model for radiative transfer: Doppler effects, equilibrium and non
equilibrium diffusion asymptotics,
with P. LAFITTE (Lille), SIAM MMS, 4(4), 1245 - 1279, 2006.
And a link to further numerical simulations.
Diffusion approximation and entropy-based moment
closure for kinetic equations,
with J.-F. COULOMBEL (Lille) and F. GOLSE (Paris 7), Asymptotic Analysis 45 (1-2), 1-39, 2005.
Stability and Asymptotic Analysis of a Fluid-Particle
Interaction Model,
with J.-A. CARRILLO (Barcelona), Comm. PDE., 31, 1349--1379, 2006.
Diffusion dynamics of classical systems driven by an oscillatory force,
with F. CASTELLA (Rennes) and P. DEGOND (Toulouse), J. Stat. Phys., 124, 913--950, 2006.
High-electric-field limit for the Vlasov-Maxwell-Fokker-Planck system
,
with M. BOSTAN (Besancon), Ann. IHP, An. Non Lineaire, 25, 1221--1251, 2008.
Low field regime for the relativistic Vlasov-Maxwell-Fokker-Planck system; the one and one half dimensional case
,
with M. BOSTAN (Besancon), AIMS-- Kinetic and Related Models, 1 (1), 139--170, 2008.
Entropy-based moment closure for kinetic equations:
Riemann problem and invariant regions
,
with J.-F. COULOMBEL (Lille), J. Hyperbolic Diff. Eq., 3 (4), 649--672, 2006.
Shock Profiles for Non Equilibrium Radiating Gases
,
with J.-F. COULOMBEL, Ch. LIN (Lille), Physica D, 218, 83--94, 2006.
Asymptotic stability of shock profiles in radiative hydrodynamics,
with J.-F. COULOMBEL, Ch. LIN (Lille),
CRAS, 345(11), 625--628, 2007.
Asymptotic problems for wave-particle interactions;
quantum and classical models
,
with F. CASTELLA (Rennes), P. DEGOND (Toulouse), Nonlinearity 20, 1677--2720, 2007.
Large time dynamics of a classical system subject to a fast varying
force,
with F. CASTELLA (Rennes), P. DEGOND (Toulouse),
Comm. Math. Phys., 276, 23--49, 2007.
Numerical schemes of diffusion asymptotics and moment closure for kinetic equations
,
with J. A. CARRILLO (ICREA, UABarcelona), P. LAFITTE (Lille), F. VECIL (UABarcelona),
in J. Sci. Comp. 35, 113--149, 2008.
On the Shockey-Read-Hall model: generation and recombination in semiconductors,
,
with V. MILJANOVIC, Ch. SCHMEISER (Univ. Wien),
SIAM J. Appl. Math., 67, 1183--1201, 2007.
Regularity analysis for systems of reaction-diffusion equations,
,
with A. VASSEUR (Austin),
Annales de l 'ENS, 43 (1), 117--141, 2010.
An Hybrid Finite Volume-Finite Element Method for Variable Density Incompressible Flows
,
with C. CALGARO (Lille) and E. CREUSE (Valenciennes), J. Comput. Phys., 227, 4671--4696, 2008.
Simulation of Fluid & Particles Flows:
Asymptotic Preserving Schemes for Bubbling and
Flowing Regimes
,
with J. A. CARRILLO (Barcelona) and P. LAFITTE (Lille), J. Comput. Phys., 227, 7929--7951, 2008.
A model describing the growth and the
size distribution of multiple metastatic
tumors
,
with A. DEVYS and P. LAFITTE (Lille), DCDS-B, 12, 4, 731--767, 2009.
Boundary value problems
for the linear Boltzmann equation involving a variable force field,
with
M. BOSTAN (Besancon), I. M. GAMBA and A. VASSEUR (Austin),
Indiana Univ. Math. J., 59(5), 1629--1660, 2010.
Stochastic acceleration in an inhomogenous time random force field,
with M. ROUSSET (Lille),
Applied Mathematics Research eXpress, 2009:1--46, 2009.
On hydrodynamic models for LEO
spacecraft charging,
with C. BESSE, S. BORGHOL, I. VIOLET (Lille)
and J.-P. DUDON (Thales),
in Some Problems on Nonlinear Hyperbolic Equations and Applications,
The French-Chinese Summer Institute on Applied Mathematics held at Fudan University,
Shanghai, September 1-21, 2008. Edited by Ta-Tsien Li, Yue-Jun Peng, Bopeng Rao.
Series in Contemporary Applied Mathematics, CAM15,
World Scientific, 2010
Modeling and simulation of fluid-particles
flows,
with P. LAFITTE, M. ROUSSET (Lille), in Some Problems on Nonlinear Hyperbolic Equations and Applications'
The French-Chinese Summer Institute on Applied Mathematics held at Fudan University,
Shanghai, September 1-21, 2008. Edited by Ta-Tsien Li, Yue-Jun Peng, Bopeng Rao.
Series in Contemporary Applied Mathematics, CAM15,
World Scientific, 2010
Comparison of Vlasov solvers for spacecraft charging simulation,
with C. BESSE, N. VAUCHELET (Lille)
J.-P. DUDON (ThalesAleniaSpace),
Math. Modelling and Numerical Analysis (M2AN), 44, 109--131, 2010.
The Navier-Stokes-Vlasov-Fokker-Planck system near equilibrium,
with A. MOUSSA (ENS Cachan), L. HE, P. ZHANG (Beijing),
SIAM J. Math. Anal., 42 (5) 2177--2202, 2010
L infinity stability of vertex-based MUSCL finite volume schemes
on unstructured grids;
simulation of
incompressible flows with high density ratios,
with C. CALGARO, E. CHANE-KANE, E. CREUSE (Lille),
J. Comput. Phys., 229 (17), 6027--6046, 2010.
On a generalized Boltzmann equation for non-classical particle transport,
with M. FRANK (Kaiserslautern), AIMS--Kinetic and Related Models, 3(3), 395--408, 2010.
Scaling limit of a discrete prion dynamics model,
with M. DOUMIC, T. LEPOUTRE (INRIA Rocquencourt), Comm. Math. Sci. 7(4), 839--865, 2009.
The linear Boltzmann equation with space periodic electric field
,
with M. BOSTAN (Besancon), I. GAMBA (U. Texas Austin)
"Nonlinear Partial Differential Equations
and Related Topics'', Dedicated to Nina N. Uraltseva, edited by A. Arkhipova and A. Nazarov, AMS Transl. Series 2, vol. 229, 51-66, 2010.
Fluid-particles flows: A thin spray model with energy
exchanges,
with L. BOUDIN (P6), B. BOUTIN (P6), B. FORNET (Onera), P. LAFITTE (Lille), F. LAGOUTIERE (P7), B. MERLET (P13)
ESAIM: Proc., 28, 195--210, 2009.
High field regimes and non standard shock relations in semiconductor superlattices
theory,
with J. J. NIETO, O. SANCHEZ and J. SOLER (Granada), to appear in SIAM J. Appl. Math.
Derivation of a non-local model for diffusion asymptotics;
Application to radiative transfer problems,
with C. BESSE (Lille), Comm. in Comput. Physics, 8, 1139--1182, 2010.
Signal propagation of the MAPK cascade in Xenopus oocytes : role of bistability and ultrasensitivity for a mixed problem,
with J.-F. BODART, R. BLOSSEY, A. DEVYS, P. LAFITTE (Lille), J. Math. Biol. (published on-line Feb. 2011).
On the Spitzer-Harm regime and non local approximations: modeling, analysis and numerical simulations,
with M. PARISOT (Lille), SIAM MMS, 9, 568--600, 2011.
Hydrodynamic regimes, Knudsen layer,
numerical schemes: Definition of boundary fluxes
with
C. BESSE, S. BORGHOL, I. LACROIX-VIOLET (Lille) and
J.-P. DUDON (Thales-Cannes) Adv. Appl. Math. Mech. (AAMM),
3(5), 519--561, 2011.
Global existence to the equilibrium diffusion model in
radiative hydrodynamics,
with C. LIN (Hohai Univ., Nanjing), Chinese Annals of Math. Series B, 32(4), 549--568, 2011.
The Lifschitz-Slyozov equation with space-diffusion of monomers,
with F. LAGOUTIERE (Paris-Sud) and L. M. TINE (Lille & St Louis Senegal),
AIMS--Kinetic and Related Models, 5(2), 325--355, 2012.
Numerical approximation of Knudsen layer for Euler-Poisson system,
with F. CHARLES, N, VAUCHELET (P6), C. BESSE, I. VIOLET (Lille), J.-P. DUDON (Thales) and L. NAVORET (Toulouse),
ESAIM: Proc. CEMRACS'10 research achievements: Numerical modeling of fusion, 32, 177--194, 2011.
Simulation of fluid--particles flows: heavy particles, flowing regime and asymptotic--preserving schemes,
with S. JIN and B. YAN (UW--Madison), Comm. Math. Sci., 10(1), 355--385, 2012.
Asymptotic-Preserving schemes for kinetic-fluid modeling of
disperse two-phase flows,
with S. JIN and B. YAN (UW--Madison) and J.-G. LIU (Duke), J. Comput. Phys. 246, 145-164, 2013
Asymptotic-Preserving schemes for kinetic-fluid modeling of disperse two-phase flows with variable fluid density,
with S. JIN and B. YAN (UW--Madison) and J.-G. LIU (Duke).
Simulations of the Lifshitz-Slyozov equations: the role of coagulation
terms in the asymptotic behavior,
with F. LAGOUTIERE (Paris-Sud) and L. M. TINE (Lille & St Louis S\'en\'egal)
M3AS, 23, 7, 1177-1215, 2013.
Finite Volume Schemes on Unstructured Grids for
Non-Local Models: Application to the Simulation of Heat
Transport in Plasmas
with M. PARISOT (Lille),
J. Comput. Phys. 231, 8188-8208, 2012.
Analysis of large amplitude shock profiles for non-equilibrium radiative hydrodynamics: formation of Zeldovich spikes
with J.-F. COULOMBEL (Nantes), P. LAFITTE (Paris), C. LIN (Hohai Univ., Nanjing),
Shock Waves, 22(3), 2012.
Positivity-preserving schemes for Euler equations:
sharp and practical CFL conditions
with C. CALGARO, E. CREUSE (Lille), Y. PENEL(P6), J. of Comput. Phys., 234, 417-438, 2013.
Numerical homogenization of nonlinearly coupled elliptic--parabolic system, reduced basis method, and application to nuclear waste storage
with A. GLORIA (Lille) and S. KRELL (Nice), M3AS, 2013.
The lovebirds problem: why solve Hamilton-Jacobi-Bellman equations matters in love affairs
with P. LAFITTE (Paris).
Simulation of Mixture Flows : Pollution Spreading and Avalanches
with C. CALGARO and E. CREUSE (Lille).
