Asymptotics, Numerics, Analysis 
of the network 


Sites of A1  WPI Vienna + Linz, Bayreuth, (ETH ZÃ¼rich), Praha, Haifa, Tel Aviv 
URL  http://www.unibayreuth.de/departments/math/org/mathe6/staff/memb/grein/hykea1/a1team.php 
Team Organizer  G. Rein 
The team A1 has been active in the mathematical modeling of physics and engineering problems with partial differential equations, their analysis and numerics for more than 15 years. Main areas of research are: semiconductor modeling, fluid dynamics, mathematical analysis of quantum transport, dispersive equations, homogenization and numerical analysis of SchrÃ¶dinger type equations, geometric singular perturbation theory, inverse problems, kinetic formulations of PDEs, analysis and numerics of hyperbolic conservation laws, variational techniques, nonlinear diffusion equations, logarithmic Sobolev inequalities, stability of steady states, ...
The team has a strategic role in the network, as its research contribution stands in the cross line of (quantum) kinetic theory and hyperbolic theory. The Linz node is an important center of inverse problems in industrial mathematics with links to a strong"scientific computing center" and long term collaborations with steel industry etc.Â
The ETH ZÃ¼rich node which has valuable experience in numerics of hyperbolic equations, participates without funding.
The team members have extensive experience in running large projects (Wittgenstein prize, two START prize projects) and have been key figures in the previous HCM and TMR network. The Vienna node carries a "doctoral school" on "Differential equations with applications", which imbeds the network training in the national PhD programme. This gives an additional link with the strong Austrian school in biomathematics that is part of the doctoral school.
The team A1 has longstanding research links within the proposed network, in particular with the following network teams : F1 (dispersive equations, nonlinear diffusion), F2 (weak coupling limits), F3 (homogenization, quantum kinetics, Wigner functions), F4 (entropy methods), D1 (open quantum systems), E2 (nonlinear diffusion), I3 (numerical analysis of SchrÃ¶dinger equations, nonlinear diffusion), S1 (asymptotics of convectiondiffusion equations).
The team A1 has done significant work in connection with the following topics contained in the work programme (topic in bold face, non exhaustive )
adÂ 1Â : analysis of various kinetictomacroscopic limits for semiconductors and plasmas,
adÂ 3Â : entropy techniques for kinetic and diffusive systems, particularly in developing and adapting the BakryEmery approach for nonlinear diffusionconvection problems,
adÂ 6 ,Â 9Â : adaptation of the Wigner formalism to general linear and weakly nonlinear dispersive equations, use of Wignerfunction techniques for open quantum systems, analysis of quantum FokkerPlanck equations,
adÂ 11Â : geometric singular perturbation theory,
adÂ 14Â : analysis of (in)compressible fluid models, in particular Navier Stokes equations,
adÂ 15Â : numerical analysis for hyperbolic systems.
The key scientific staff consists of the following members :
 N. J. Mauser (CO) (WPI, U. Wien, 20%)  G. Rein (TO) (WPI, U. Wien, 30%)  P. A. Markowich (SC) (WPI, U. Wien 20%)  C. Schmeiser (WPI, TUWien, 20%)  P. Szmolyan (WPI, TUWien, 20%)  H. Engl (IAB) (U. Linz, 15%)  W. Burger (U. Linz, 20%)  R. Jeltsch (ETH ZÃ¼rich, 15%)  J. Necas (U. Praha, 20%)  J. Malek (TC) (U. Praha, 20%)  M. Rokyta (U. Praha, 20%)  E. Feireisl (Academy Praha, 20%)  S. Necasova (Academy Praha, 20%)  H. Petzeltova (Academy Praha, 20%)  G. Wolanski (Technion, Haifa 20%);  E. Tadmor (SAB) (Tel Aviv U. and UCLA, 15%)
The two most significant publications for the IHP project are the following:
[1] P. GÃ©rard (F2), P. A. Markowich (A1), N. J. Mauser (A1), and F. Poupaud (F3),Â Homogenization limits and Wigner transformsÂ , Comm. Pure Appl. Math.,Â 50Â (1997), pp. 323379.
[2] M. Escobedo (E2), Ph. LaurenÃ§ot (F3) and E. Feireisl (A1),Â Large time behavior for degenerate parabolic equations with dominating convective termsÂ , Comm. P.D.E.Â 25Â , no. 12 (2000), 7399