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# Short presentation of the team E2

 Sites of E2 Granada + Sevilla, Madrid (Autonoma, Carlos III), Barcelona, Lisboa URL http://www.ugr.es/~kinetic/ Team Organizer J. Soler

The research of the Granada team (constituted by groups at the Universities of Granada, AutOnoma de Madrid, Carlos III de Madrid, Lisboa and Sevilla) consists of multidisciplinar studies of asymptotic techniques for various transport P.D.E. arising in combustion, kinetic and quantum-mechanical problems. The Granada team also keeps good scientific connections with a great deal of teams of our network (for instance the teams A1, F1, F3, F4, I3, etc.).

Topics on which the Granada team has previous experience are closely related to the objectives programmed in the work plan, especially:

1) Quantum-kinetic transport models. We have studied widely used models for formation and dynamics of electric field domains and self-sustained oscillations of the current through the devices. (nonlinear drift-diffusion equations or differential-difference equations and their hyperbolic limits, task 2 ). From a different point of view, some qualitative aspects (scaling limits, long time behavior, existence and uniqueness of solutions, etc.) of general Schrödinger and Wigner-type systems have been developed, in particular for Schrödinger-Poisson, Wigner-Poisson, Wigner-Poisson-Fokker-Planck and Schrödinger-Poisson-Slater (X$\alpha$-approximation) equations (task 6 ).

2) Transport kinetic equations (task 7 ) of nonlinear Fokker-Planck and Vlasov-Poisson-Fokker-Planck types (long time behavior, stability and bifurcation of different solutions, reduction by Chapman-Enskog methods, etc.) have been tackled. Our group has also experience in the analysis of kinetic equations with different collision kernels: Boltzmann-type, Fokker-Planck, wave-particle and random collision kernels related to the Boltzmann equation.

3) In Granular flows (task 10 ) we have worked on: reduction of kinetic equations for fast granular flows in the hydrodynamic limit (cooling, Faraday instability, etc.). We have also worked on granular flows on quasifluid regimes (proposing model equations, recognizing parameters from experimental data and solving numerically the equations) with applications to granular flows in silos.

4) The Granada team also has some experience in the study of P.D.E. which arise in combustion theory and detonation problems: (asymptotic and numerical methods for homogeneous explosions and overdriven detonations, free boundary problems, fully nonlinear parabolic equations, control aspects, thermal avalanche, etc.)

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

- J. Soler (TO) (U. Granada, 35%);  - M. J. Caceres (U. Granada, 25%);  - J. A. Carrillo (U. Granada, 25%);  - P. Garrido (U. Granada, 25%);  - J. L. Lopez (U. Granada, 25%);  - E. Ruiz Arriola (U. Granada, 25%);  - J. Brey (U. Sevilla, 25);  - M. J. Ruiz-Montero (U. Sevilla, 25%);  - L. L. Bonilla (U. Carlos III, 25);  - M. Kindelan (U. Carlos III, 25%);  - M. Moscoso (U. Carlos III, 25);  - G. Platero (CSIC, 25%);  - F. Quiros (U. Autonoma de Madrid, 25%);  - J. L. Vazquez (SAB) (U. Autonoma de Madrid, 25%);  - M. C. Carvalho (U. Lisboa, 25%).

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

[1] E. A. Carlen, M. C. Carvalho (E2), E. Gabetta (I3), Central Limit Theorem for Maxwellian molecules and Truncation of the Wild sum , Comm. in Pure and Appl. Math., 53 (2000) 370--397.

[2] J. Nieto (E2), F. Poupaud (F3), J. Soler (E2), High-Field Limit for the Vlasov-Poisson-Fokker-Planck System , to appearin Arch. Rat. Mech. Anal. (2001).

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