HYperbolic and Kinetic Equations :
Asymptotics, Numerics, Analysis
of the




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Short presentation of the team F2

Sites of F2 ENS Ulm + Paris 6, X, INRIA, Lille
Team Organizer F. Golse

This group has been heavily involved for more than ten years in developing some of the modern analytical tools for kinetic models and conservation laws - such as smoothing by velocity averaging, dispersion and Strichartz estimates for transport equations with applications to the smoothness of solutions of the Vlasov-Poisson system, kinetic formulations of (systems of) conservation laws... In all satellites of the F2 group, different themes of the work program are represented, a circumstance that fostered intense cooperation, such as the working seminar on problems of geometrical optics (task 13 of the work program) involving the group of applied mathematics at ENS Ulm, J.-D. Benamou from INRIA and researchers from CEA (the French Atomic Energy Commission) organized bi-monthly at ENS Ulm in 1999-2000. Likewise, a GDR (research network at the national level operated by CNRS, the French agency of scientific research) focussed on the modelling, mathematical analysis and scientific computing of the dynamics of charged particles (task 2 of the work program) involved the teams from ENS Ulm, Ecole Polytechnique and Paris 6 in a significant way and promoted their interactions with industrial partners (such as CEA, Thomson...)

A traditional theme for this group is that of macroscopic limits of kinetic or particle models, with applications to kinetic schemes. This theme intersects with tasks 1 , 2 , 8 , 9 and 10 of the work program and has involved most of the participants (in particular Allaire, Bouchut, Coquel, Golse, Lucquin, Paul, Perthame, Saint-Raymond) and collaborators from groups A1, G1, I1, I3, S1, S2. More classical aspects of the mathematical analysis of hyperbolic systems of conservation laws, such as described in tasks 11 and 12 of the work program, are represented mainly by LeFloch, with collaborations with group I2. Various aspects of modelling, in connection with tasks 2 , 5 , 7 , 10 and 13 of the work program currently involve Allaire, Benamou, Golse, Lucquin, Perthame, Saint-Raymond), with again intensive interaction with groups D2, E1, I1, S1. Finally, the group also has a strong component of numerical analysis that ranges from the theoretical analysis of numerical schemes such as in tasks 1 and 15 to scientific computing such as in tasks 5 and 16 (involving in particular Allaire, Bristeau, Bouchut, Coquel, Despres, Perthame, and collaborations with groups D2, E1, G1, I1, I3, S1, S2 and with EDF - the French electricity agency - as industrial partner). The key scientific staff consists of

- F. Golse (TO) (ENS Ulm & Paris 6, 25%),  - F. Bouchut (ENS Ulm, 25%),  - T. Paul (ENS Ulm, 20% ),   - C. Bardos (Paris 6, 60%),  - F. Coquel (Paris 6, 30% ),  - B. Despres (Paris 6, 20%),   - B. Lucquin (Paris 6, 30% ),  - B. Perthame (SiC) (Paris 6, 25%),   - L. Saint-Raymond (Paris 6, 20% ),  - G. Allaire (IAB) (Ecole Poytechnique, 20% ),   - P. Le Floch (Ecole Poytechnique, 20% ),  - J.D. Benamou (INRIA, 20% ),   - M.O. Bristeau (INRIA, 20 %)  

Among the most significant publications of this group, one can quote

[1] Bressan, Alberto (I2); LeFloch, Philippe G. (F2): Structural stability and regularity of entropy solutions to hyperbolic systems of conservation laws. Indiana Univ. Math. J. 48 (1999), no. 1, 43--84.

[2] Bourgain, Jean; Golse, François (F2); Wennberg, Bernt (S1): On the distribution of free path lengths for the periodic Lorentz gas. Comm. Math. Phys. 190 (1998), no. 3, 491-508.

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HYperbolic and Kinetic Equations: Asymptotics, Numerics, Analysis - HYKE