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Pré-publications :
35 :
F. Berthelin, Particle approximation of initial
data for systems of conservation laws in two dimensions
Preprint,
submitted (2024)
Publications
:
34 :
F. Berthelin, Existence result for a
two-dimensional system of conservation laws with unilateral
constraints
Nonlinear
Analysis, vol.
232,
(2023), article
113248
33 : F.
Berthelin, Solution of kinetic
equations related to non-local conservation laws
Journal of Hyperbolic Differential Equations, vol.
20, No. 1
(2023), 119-154
32 : P.
Amorim, F. Berthelin, T. Goudon, A
non-local scalar conservation law describing navigation
processes
Journal of
Hyperbolic Differential Equations, vol. 17, No.4 (2020), 809-841
31: F.
Berthelin, P. Goatin, Regularity
results for the solutions of a non-local model of traffic flow
Discrete
Contin. Dyn. Syst. 39
(2019), no. 6, 3197–3213
30: F.
Berthelin, J. Vovelle, Stochastic isentropic
Euler equations
Annales
scientifiques de l'ENS
(4)
52 (2019), no.
1, 181–254.
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
KRM,
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
JMPA, 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
KMR, 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. Berthelin, Existence
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, 694 pages.
Equations différentielles pour la licence, le master et
l'agrégation. Cours complet, 190 exercices corrigés et 90
figures.
Seconde édition, 2021, 714 pages
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.
