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Asymptotics, Numerics, Analysis
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Short presentation of the team S1

Sites of S1 Gothenburg + Chalmers, Karlstad, Warsaw, Wroclaw, Zielena Gora
URL http://www.md.chalmers.se/Math/Research/Kinetics/Hyke_got/
Team Organizer B. Wennberg

The Gothenburg team consists of groups in Gothenburg (Swe), Karlstad (Swe), Wroclaw (Pl), Warsaw (Pl) and Zielena Gora (Pl). It is a large group with an experience in kinetic theory as well as the theory of hyperbolic equations. The link between Gothenburg and Warsaw, and with Pr. Bobylev in Karlstad. The group in Wroclaw has tight links with Zielona Gora, but there is also a cooperation with the Warsaw group. The team has a long record of contacts with several of the other teams in the network, some of which is mentioned below.

The groups in Gothenburg, Karlstad, Warsaw have a strong experience in the mathematical and numerical analysis of kinetic equations. Questions of particular interest to the groups are boundary value problems (in strong cooperation with F3), long time asymptotics as well fluid asymptotics (tasks 3 , 7 ), and also problems related to general relativity (e.g. together with D2). Discrete velocity models are studied e.g. in collaboration with I3 (this is partially motivated by numerical analysis).

The group has experience in modelling granular flows, and of coagulation-fragmentation (tasks 5 and 10 ). This research has been carried in different collaborations with E2 (granular media) and with F3 (coagulation, Becker-Doring model).

The team is also experienced in numerical analysis of kinetic equations (in particular discrete velocity models, and direct methods, task 15 , 16 ). This is done in collaborations within the team, and otherwise with D1. A "kinetic method" for mean curvature driven flows is being developed (task~ 13 ), partially in collaboration with Summus Limited, North Carolina, USA . This has applications e.g. in image processing. The group has also a strong knowledge in finite element analysis.

The groups in Wroclaw and Zielona GOra have a long time experience in the field of nonlocal elliptic problems and the asymptotic behaviour of evolution PDE:s. Applications of this are, for example, the modelling of carrier transport in semiconductors and electrolytes, energy-transport models and hydrodynamic-type equations with for example Lévy type diffusion. Recent results are about steady states and blow-up of solutions (pertaining to tasks 3 , 8 ), work is carried out on convection-diffusion systems, and viscous Hamilton-Jacobi equations (task 8 , 13 ). There is a strong cooperation with the teams F1 and A1.

The Warsaw group also has a long term experience in various aspects of mathematical theory of micropolar fluids.

The key scientific staff consists of

- B. Wennberg (TO) (Go, 25%);  - L. Arkeryd (SAB) (Go, 25%);  - H. Andreasson (Go, 25%);  - M. Asadzadeh (Go, 25%);  - A. Heintz (Go, 25%);  - R. Pettersson (Go, 25%);  - S. Barza (Ka, 25%);  - A. Bobylev (Ka, 25%);  - C. Uggla (Ka, 25%);  - A. Palczewski (Wa, 25%);  - M. Lachowicz (Wa, 25%);  - G. Lukaszewicz (Wa, 25%);  - T. Platkowski (Wa, 25%);  - D. Wrzosek (Wa, 25%);  - P. Bile r (Wr, 25%);  - G. Karch (Wr, 25%);  - T. Nadzieja (Z G, 25%).

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

[1] P. Biler (S1), J. Dolbeault (F1), M.J. Esteban (F1), G. Karch (S1): Stationary solutions, intermediate asymptotics and large time behaviour of type II Streater's models, Adv. Diff. Eq. 6 (2001), 461--480.

[2] A.V. Bobylev (S1), J. A. Carillo (E2), I. Gamba: On some properties of kinetic and hydrodynamic equations for inelastic interactions, J. statist. Phys. 98 (2000), 743-773.



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HYperbolic and Kinetic Equations: Asymptotics, Numerics, Analysis - HYKE