Asymptotics, Numerics, Analysis 
of the network 


Sites of I1  L'Aquila + Roma: IACCNR, "La Sapienza", "Tor Vergata" 
URL  http://univaq.it/~hyke 
Team Organizer  P. Marcati 
The team Italy 1 (I1) has a long time experience of research concerning relaxation problems for nonlinear hyperbolic systems and the related asymptotic analysis including convergence, singular limit study and singular phenomena as the initial and the boundary layer.
Mathematical methods, which includes functional analytic tools and classical analysis tools, have been used with success in this framework. Applications dealing with the mathematical modeling of porous media flows and the hydrodynamic modeling of semiconductors devices (task 1 ) have been widely investigated. More recently the L'Aquila node and the Roma IACCNR node have extensively investigated relaxation problems leading to the approximations of nonlinear parabolic systems (tasks 1 and 15 ).
This mathematical toolbox allows the asymptotic analysis of BGK type approximations (task 1 ). Collaboration in this area (which led to published papers or preprints) already exists with team F1, F2, F3, F4, D1, D2 and G1. Potential future collaboration in these topics can be expected with A1 and S2. Numerical methods exploiting the previous mathematical ideas (task 15 ), in particular BGK approximations, have been developed with the Roma IACCNR node and F3.
The Roma "La Sapienza" node supplemented by people in L'Aquila has a recognized expertise in classical kinetic theories (tasks 8 and 9 ) and more recently they have been very active in developing the investigation of mathematical models for granular flows (task 10 ). Some of the results achieved in this area are quite encouraging for future research. Collaborations have been established by many years with F2 and F4 and potentially G1.
Particle type approximations, mesoscopic limits and deduction of macroscopic limit models have been considered by many people in L'Aquila and Roma nodes via analytical and probabilistic tools (tasks 7 , 8 and 9 ). Moreover, in the Roma IACCNR node there is wide experience concerning applications of these ideas to numerical simulations by using Lattice Boltzmann equation to approximate fluid dynamic models (tasks 15 and 16 ). Collaboration exists in part of these topics with F2 and D1. Other fluid models investigated in the Roma IACCNR node and L'Aquila node concern traffic flows, void formations in chemical reactors, oil pollution of shallow waters, mechanicalmathematical and numerical modeling of moisture transport and damage evolution in porous NBS (tasks 2 , 4 , 5 , 7 and 16 ). Some collaborations on this last topic started with G1.
Theoretical problems having high impact on the applications such as the analysis of nonclassical shocks, blow up of solutions, stability analysis of nonlinear waves (task 11 and 12 ) are investigated by people in Roma and L'Aquila nodes. Some collaborations exists with F2, D2, S2.
The key scientific staff consists of the following members:
 M. Pulvirenti (U. Roma La Sapienza, 30%);  P. Marcati (TO, SC) (U. L'Aquila, 30%);  A. de Masi (U. L'Aquila, 20%);  R. Esposito (U. L'Aquila, 20%);  V. Georgiev (U. L'Aquila, 20%);  B. Rubino (U. L'Aquila, 30%);  A. Teta (U. L'Aquila, 20%);  S. Claudi (U. L'Aquila, 30%);  D. Donatelli (U. L'Aquila, 30%);  F.R. Guarguaglini (U. L'Aquila, 30%);  E. Caglioti (U. Roma La Sapienza, 20%);  C. Marchioro (U. Roma La Sapienza, 20%);  M. Pulvirenti (U. Roma La Sapienza, 30%);  R. Natalini (TC) (Roma IACCNR, 30%);  P. Piccoli (Roma IACCNR, 20%);  S. Succi (Roma IACCNR, 20%);  C. Sinestrari (U. Roma Tor Vergata, 25%);  R. Marra (U. Roma Tor Vergata, 20)%).
The two most significant publications for the IHP project are the following:
[1] P. Marcati, B. Rubino, Hyperbolic to parabolic relaxation theory for quasilinear first order systems , J. Differential Equations, 162 (2000), pp. 359399.
[2] S. Bastea, R. Esposito, J.L. Lebowitz, R. Marra, Binary fluids with long range segregating interaction. I. Derivation of kinetic and hydrodynamic equations. J. Statist. Phys. 101 (2000), pp. 10871136