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SMAI Journal of Computational Math.

A SMAI publication supported by CNRS, Inria, free of charge for readers and authors.

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Mathematics for modeling and scientific computing
Wiley

Modeling and Scientific Computing

Integration:
Integrale de Lebesgue et introduction a l'analyse fonctionnelle, Editions Ellipses

Integration

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Version: 1.0
(November 25, 2007)

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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), Trans. AMS, 359, 637-648, 2007.
  • 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.
  • Non-local macroscopic models based on Gaussian closures for the Spitzer-Harm regime with M. PARISOT (Lille), AIMS--Kinetic and Related Models, 4(3), 735--766, 2011.
  • 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.
  • A fluid-kinetic model for particulate flows with coagulation and breakup : stationary solutions, stability and hydrodynamic regimes, with L. M. TINE (Paris 5 & St Louis, Senegal) and M. SY (St Louis, S?en?egal), SIAM. J. Appl. Math., 73 (1), 401-421, 2013.
  • Analysis of the M1 model : well-posedness and diffusion asymptotics, with C. LIN (Hohai Univ., Nanjing & Shanghai Jiatong Univ.) J. Math. Anal. Appl., 402 , no. 2, 579-593, 2013.
  • The lovebirds problem: why solve Hamilton-Jacobi-Bellman equations matters in love affairs with P. LAFITTE (Paris), Acta. Appl. Math.
  • Modeling and simulation of mixture flows: Application to powder--snow avalanches with C. CALGARO and E. CREUSE (Lille), Computers and Fluids, 107, pp.100-122, 2015.
  • Kinetic schemes on staggered grids for barotropic Euler models : entropy- stability analysis, with F. BERTHELIN and S. MINJEAUD (Nice) Math. of Comp., 84 (295), pp. 2221--2262, 2015.
  • A Semi-Lagrangian approach for dilute non-collisional fluid-particle flows, with A. CHAMPMARTIN (Inria Sophia), C. FOCHESATO, J.-P. BRAEUNIG (CEA).
  • Consistency analysis of a 1D Finite Volume scheme for barotropic Euler models, with F. BERTHELIN and S. MINJEAUD (Nice), Proc. FVCA 7, Berlin 2014.
  • Self-organized populations interacting under pursuit-evasion dynamics, with B. NKONGA, M. RASCLE, M. RIBOT (Nice), Phys. D, 304--305, pp. 1--22, 2015.
  • Multifluid flows: a kinetic approach, with F. BERTHELIN and S. MINJEAUD (Nice), J. Sci. Comput., 66(2) pp 792--824, 2016.
  • On a Model for Mixture Flows: Derivation, Dissipation and Stability Properties, with A. VASSEUR (Austin, USA), Archiv. Rat. Mech. Anal., 220(1), pp. 1--35, 2016.
  • Damping of particles interacting with a vibrating medium , with A. VAVASSEUR (Nice) and R. ALONSO (PUC, Rio).
  • From Vlasov-Poisson and Vlasov-Poisson-Fokker-Planck Systems to Incompressible Euler Equations: the case with finite charge , with J. BARRE, D. CHIRON (Nice) and N.MASMOUDI (CIMS, NYU), J. Ecole Polytechnique, 2, pp. 247-296, 2015.
  • Efficient numerical calculation of drift and diffusion coecients in the diffusion approximation of kinetic equations, with V. BONNAILLIE-NOEL (ENS Paris) and J.A. CARRILLO, G. A. PAVLIOTIS (Imperial College at London), IMA J. Numerical Analysis, 2016.
  • Analysis of a chemotaxis system modeling ant foraging, with P. AMORIM (U. Federal Rio) and R. ALONSO (PUC Rio), Math. Models Methods Appl. Sc., 26(9), pp. 1785--1824, 2016.
  • Analysis of kinetic and macroscopic models of pursuit–evasion dynamics, with L. URRUTIA (Granada, Spain), to appear in Comm. Math. Sci.
  • Mean field limit for particles interacting with a vibrating medium, with A. Vavasseur (Nice), to appear in Annali Univ. Ferrara.
  • Simulations of non homogeneous viscous flows with incompressibility constraints, with C. Calgaro, E. Creuse (Lille) and S. Krell (Nice), to appear in Math. and Computers in Simulation.
  • Particles interacting with a vibrating medium: existence of solutions and convergence to the Vlasov--Poisson system, with S. De Bievre (Lille) and A. Vavasseur (Nice), to appear in SIAM J. Math. Anal.