Asymptotics, Numerics, Analysis 
of the network 


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 quantummechanical 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) Quantumkinetic transport models. We have studied widely used models for formation and dynamics of electric field domains and selfsustained oscillations of the current through the devices. (nonlinear driftdiffusion equations or differentialdifference 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 Wignertype systems have been developed, in particular for SchrödingerPoisson, WignerPoisson, WignerPoissonFokkerPlanck and SchrödingerPoissonSlater (X$\alpha$approximation) equations (task 6 ).
2) Transport kinetic equations (task 7 ) of nonlinear FokkerPlanck and VlasovPoissonFokkerPlanck types (long time behavior, stability and bifurcation of different solutions, reduction by ChapmanEnskog methods, etc.) have been tackled. Our group has also experience in the analysis of kinetic equations with different collision kernels: Boltzmanntype, FokkerPlanck, waveparticle 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. RuizMontero (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) 370397.
[2] J. Nieto (E2), F. Poupaud (F3), J. Soler (E2), HighField Limit for the VlasovPoissonFokkerPlanck System , to appearin Arch. Rat. Mech. Anal. (2001).