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




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Short presentation of the team F1

Sites of F1 Dauphine + Orsay, ENS-Cachan, CERMICS, Versailles, Evry, Orléans, Tours
URL http://www.ceremade.dauphine.fr/~dolbeaul/Hyke/F1.html
Team Organizer J. Dolbeault

The F1 team is made of several groups belonging to universities (Dauphine, Orsay, Evry, Orléans, Versailles), schools and research centers ( Cachan, CERMICS), which have been very active in the study of partial differential equations arising from physics.

The main resarch areas of the F1 team that are concerned with the project (tasks 2 , 3 , 5 , 6 , 7 , 8 , 9 , 10 , 12 , 13 , 15 , 16 ) are:

Kinetic Equations : existence and regularity theory (including the case of Boltzmann and Landau equations, and collisional or dispersive models for bosons), kinetic formulations and relaxation methods for systems of conservation laws, gases without pressure, numerical methods for collision operators and multiscale analysis of models of charged particles, entropy dissipation methods for the long time asymptotics of diffusive systems,

Fluid Dynamics : weak solutions for fluid mechanics and fluid-structure interactions, fluids with polymers, dirty fluids (with particles or agregates), particle and finite element methods for compressible or incompressible fluids.

PDEs of Quantum Mechanics : stationary or time dependent equations for quantum chemistry, large time, semi-classical and thermodynamical (crystals) limits, semiclassical limits and homogenization (Wigner measures, WKB analysis), eigenvalue crossings, geometric optics for very high frequency waves in inhomogeneous media, Hamilton-Jacobi type equations, stability of nonlinear dispersive problems, numerical methods and relativistic models for quantum chemistry.

The team has a strong experience of collaborations and training through bilateral agreements and european networks (TMR). Through already existing collaborations, it is expected to contribute in the development of entropy dissipation techniques (A1, D1, S1 Wroclaw, E1 Bilbao), in stability analysis (F3 Toulouse, F4 Rennes, E2), in the derivation of linear kinetic equations from particle models with obstacles (I1 Roma"La Sapienza"), in the study of granular media (I1 Roma"La Sapienza", I2, I3 and I3 Politecnico di Milano, S1 Karlstad), of multiscale phenomena for charged particles systems (A1, F3), of fluid mechanics and fluid-structure interactions (F4, E1 Bilbao, E2), of collisional models for sprays and of fluids with polymers and dirty fluids (F2). The group should also play a leading role in the study of equations of quantum mechanics (A1, F3), of Hamilton-Jacobi equations and nonlinear geometric optics methods (G1), with possible applications to control theory (F4 Rennes, E1 Madrid). Both theoretical and numerical (CERMICS, Orléans) points of view are well represented.

The key scientific staff consists of the following members (in brackets: project involvement in percentage of full time employment):

   - J. Dolbeault (TO) (Paris IX-Dauphine, 30%)  - P. L. Lions (Paris IX-Dauphine, 10%)  - M.J. Esteban (SAB) (Paris IX-Dauphine, 25%)  - E. Sere (Paris IX-Dauphine, 20%)   - I. Catto (Paris IX-Dauphine, 20%)  - P. Gerard (Paris Sud Orsay, 30%)  - I. Gallagher (Paris Sud Orsay, 30%)  - N. Burcq (Paris Sud Orsay, 20%)  - L. Desvillettes (ENS Cachan,30%)  - C. Le Bris (ENPC, 20%)  - S. Mischler (Versailles, 30%)  - S. Mas-Gallic (IAB) (Evry, 30%)  - L. Corrias (Evry, 30%)  - S. Cordier (Orleans, 30%)  - F. James (Orleans, 30%)  - G. Barles (Tours, 30%)  

The two most significant publications for the IHP project are the following:

[1] L. Desvillettes (F1), C. Villani (F4), On the trend to global equilibrium in spatially inhomogeneous entropy-dissipating systems. Part I : The linear Fokker-Planck equation, Comm. Pure Appl. Math. 54 (2001), no. 1, 1-42.

[2] I. Catto, C. Le Bris, P.-L. Lions, On the thermodynamic limit of Hartree-Fock type models, to appear in Ann. Inst. H. Poincaré, Anal. Non Linéaire, 2001.

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