Publications


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Pré-publications :

29 F. Berthelin, P. Goatin, Particle approximation of a constrained model for traffic flow.
                      
Accepté pour publication à NoDEA, Nonlinear Differential Equations and applications (2017).


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,  Accepté pour publication à NHM, Applied Math. Journal Networks and Heterogeneous Media (2017).

27:  F. Berthelin,  Theoretical study of a multi-dimensional pressureless model with unilateral constraint.
                       
Accepté pour publication à SIAM, Journal on Mathematical Analysis (2017).

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

Publications :

25:  F. Berthelin, T. Goudon, S. Minjeaud, Multifluid flows: a kinetic approach
                       Journal of Scientific Computing,
Springer Verlag, (2016), 66 (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), 14 (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.

 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).

 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.

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

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.

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.


Livres :

  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 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 dont 4 papiers sont issus :

N. Ayi, From Newton's law to the linear Boltzmann equation without cut-off
                

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

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