Publications


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Pré-publications :

30:  F. Berthelin, J. Vovelle, Stochastic isentropic Euler equations
                       
Accepté pour publication à Annales scientifiques de l'ENS (2017).

Publications :

29 F. Berthelin, P. Goatin, Particle approximation of a constrained model for traffic flow.
                      
NoDEA, Nonlinear Differential Equations and applications, 2017, vol. 24, no. 5, pp. 24-55.

28:  F. Berthelin, T. Goudon, B. Polizzi, M. Ribot, Asymptotic problems and numerical schemes for traffic flows with unilateral constraints describing the formation of jams,                        NHM, Applied Math. Journal Networks and Heterogeneous Media, 2017, vol. 12, no. 4, 2017.

27:  F. Berthelin,  Theoretical study of a multi-dimensional pressureless model with unilateral constraint.
                      
SIAM, Journal on Mathematical Analysis, 2017, vol. 49, no. 3, pp. 2287-2320.

25:  F. Berthelin, T. Goudon, S. Minjeaud, Multifluid flows: a kinetic approach
                       Journal of Scientific Computing,
Springer Verlag, 2016, vol. 66, no. 2, pp.792-824.

24: F. Berthelin, D. Chiron, M. Ribot, Stationary solutions with vacuum for a one-dimensional chemotaxis model with non-linear pressure
                      
Communications in Mathematical Sciences,  International Press, 2016, vol. 14, no. 1, pp.147-186.

22:  F. Berthelin, T. Goudon, S. Minjeaud, Kinetic schemes on staggered grids for barotropic Euler models: entropy-stability analysis
                       Mathematics of Computation, 84, 2015, no. 295, 2221-2262.

21:  F. Berthelin, D. Broizat, A model for the evolution of traffic jams in multi-lane
                       Kinetic and Related Models, Vol. 5, no. 4, (2012), 697-728.

19:  F. Berthelin, J. Vovelle, A BGK approximation to scalar conservation laws with discontinuous flux
                     
Proc. of the Royal Society of Edinburgh A 140 (2010), no. 5, 953–972.

 18:  F. Berthelin, S. Junca, Averaging lemmas with a force term in the transport equation
                     
Journal de Mathématiques Pures et Appliquées, Vol 93, Issue 2 (2010), 113-131.

 16:  F. Berthelin, A.E. Tzavaras, A. Vasseur,  From discrete velocity Boltzmann equations to gas dynamics before shocks
                     Journal of Statistical Physics 135 (2009), 151-173.

 15:  N. Besse, F. Berthelin, Y. Brenier, P. Bertrand, The multi-water-bag model for collisionless kinetic equations
                      Kinetic and Related Models, Vol. 2, no. 1, (2009), 39--80.

 14:  F. Berthelin, P. Degond, V. Le Blanc, S. Moutari, M. Rascle, J. Royer, A traffic-flow model with constraint for the modeling of traffic jams
                      M3AS, Mathematical Models & Methods in Applied Science, Vol. 18, No 1 (2008) 1269-1298.

13:  F. Berthelin, P. Degond, M. Delitala, M. Rascle, Model for the formation and evolution of traffic jams
                      ARMA, Arch. Ration. Mech. Anal. 187 (2008), no. 2, 185--220.

12:  F. Berthelin, N. Mauser, F. Poupaud, High-field limit from a kinetic equation to multidimensional scalar conservation laws
                      Journal of Hyperbolic Diff. Equations 4 (2007), no. 1, 123-145.

 11:  F. Berthelin, A. Vasseur, From kinetic equations to multidimensional isentropic gas dynamics before shocks
                      SIAM, Journal on Mathematical Analysis 36 (2005), no 6, 1807-1835.


10:  F. Berthelin, Convergence of flux vector splitting schemes with single entropy inequality for hyperbolic systems of conservation laws
                     Numerische Mathematik 99 (2005), no. 4,  585-604.

  8:  F. Berthelin, Numerical flux-splitting for a class of hyperbolic systems with unilateral constraint
                      M2AN, Mathematical Modelling and Numerical Analysis 37 (2003), no. 3, 479-494.

  7:   F. Berthelin, F. Bouchut, Weak solutions for a hyperbolic system with unilateral constraint and mass loss
                      Annales de l'Institut Henri Poincaré, Analyse non linéaire 20 (2003), 975-997.

  6:   F. Berthelin, F. Bouchut, Relaxation to isentropic gas dynamics for a BGK system with single kinetic entropy
                     Methods and Applications of Analysis, 9(2) (2002) 313-327.

  5:   F. Berthelin, F. Bouchut, Weak entropy boundary conditions for isentropic gas dynamics via kinetic relaxation
                     Journal of Differential Equations 185 (2002) 251-270.

  4:   F. Berthelin, F. Bouchut, Kinetic invariant domains and relaxation limit from a BGK model to isentropic gas dynamics
                     Asymptotic analysis, Vol. 31, No. 2 (2002) 153-176.

  3:  F. BerthelinExistence and weak stability for a pressureless model with unilateral constraint
                     M3AS, Mathematical Models & Methods in Applied Science, Vol. 12, No. 2 (2002) 249-272.

1:  F. Berthelin, F. Bouchut, Solution with finite energy to a BGK system relaxing to isentropic gas dynamics
                      Annales de la Faculté des Sciences de Toulouse 9 (2000), 605-630.


Manuscrits de thèse, habilitation : 

 17:  F. Berthelin,  Quelques équations cinétiques et hyperboliques : limites hydrodynamiques, modèles avec contraintes et méthodes numériques
                     
Mémoire d'Habilitation à Diriger des Recherches, Université de Nice (2009).

  2:   F. Berthelin, Relaxation  hyperbolique et modèles cinétiques en dynamique des gaz
                      Thèse, Université d'Orléans (2001), 199 pages.

Proceedings principaux : 

23:  F. Berthelin, T. Goudon, S. Minjeaud, Consistency analysis of a 1D Finite Volume scheme for barotropic Euler models, Proceedins of the 7th international symposium on Finite Volumes for Complex Applications (Berlin, Allemagne), 2014.

20:  F. Berthelin, S. Junca, Des lemmes de moyenne avec un terme de force dans l'équation de transport, Séminaire Equations aux dérivées partielles (Polytechnique) (2009-2010), Exp. No. 15, 14p.

  9:  F. Berthelin, F. Vasseur, From kinetic equations to multidimensional isentropic gas dynamics. EQUADIFF 2003, 499--501, World Sci. Publ., Hackensack, NJ, 2005.

Livre d'enseignement :

26:  F. Berthelin, Equations différentielles, Cassini, 2017.

 
Publications d'étudiants encadrés en thèse :

Thèse 1: D. Broizat, Existence, unicité, approximations de solutions d'équations cinétiques et hyperbolique
                   Thèse, Université de Nice (2013)

co-encadré avec P.E. Jabin (50-50) dont 3 papiers sont issus :

D. Broizat, A kinetic model for coagulation-fragmentation
                     Ann. Institut H. Poincaré, Analyse Non Linéaire 27 (2010) 809-836.

F. Berthelin, D. Broizat, A model for the evolution of traffic jams in multi-lane
                     Kinetic and Related Models, Vol. 5, no. 4, (2012), 697-728.

Y. Bourgaut, D. Broizat, P.E. Jabin, Convergence rate for the method of moments with linear closure relations
                      Kinetic and Related Models, Vol. 8, no. 1, (2015), 1-27.

Depuis, D. Broizat est professeur en classe préparatoire.

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Thèse 2: N. Ayi, Influence du stochastique sur des problématiques de changements d'échelle
                   Thèse, Université de Nice (2016)

co-encadré avec L. Saint-Raymond (50-50) dont 4 papiers sont issus, en particulier :

N. Ayi, From Newton's law to the linear Boltzmann equation without cut-off
                   Communications in Mathematical Physics, 350 (3), 1219-1274.

N. Ayi, High-Field Limit from a Stochastic BGK Model to a Scalar Conservation Law with Stochastic Forcing

Depuis sept 2017, Nathalie Ayi est maître de conférences à l'université Pierre et Marie Curie.