HYperbolic and Kinetic Equations :
Asymptotics, Numerics, Analysis
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Short presentation of the team D2

Sites of D2 MPI Leipzig + Aachen, Bonn, Freiburg, Heidelberg, Magdeburg, Potsdam (MPI), Regensburg, Berlin
URL http://www.mis.mpg.de/sm/hyke/
Team Organizer H. Freistühler

This team has a long experience mainly in the analytical and numerical treatment of hyperbolic problems; it has also significantly contributed to kinetic theory.

The groups in Aachen, Freiburg, and Magdeburg have contributed to the numerics of conservation law (task 15, task 16) and related applied computation, often in close cooperation with engineers (Aachen, Magdeburg) and physicists (Freiburg). An example is the intense collaboration of Krner and his group with astrophysicists (development of MHD codes); the same group has also worked with members of the French teams F3 (combined continuum/particle methods) and F2 (numerics of moving phase boundaries). The emphasis is on genuinely multidimensional schemes.

The groups in Bonn, Heidelberg, Leipzig, Potsdam, Regensburg are more analytically oriented, with equally close links to applications. Leipzig strongly represents mathematical materials science, notably micromagnetism / Hamilton-Jacobi equations (task 13). The groups in Leipzig and Heidelberg have made contributions to the stability analysis of shock waves (task 12) and relaxation approximation of conservation laws (task 1), partly in cooperation with members of the teams F4 and I1; theoretical results on dynamic phase transitions have been obtained with members of I2 and F4, results on MHD shock waves with A1. The team in Bonn has important results on hydrodynamic limits (task 1) together with team F4. Team members from Bonn and Leipzig have established resul ts on the vanishing viscosity limit (task 11). The groups in Potsdam and Regensburg have had a significant long-term production of mathematical results in relativistic (task 14) and quantum evolution problems (task 6).

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

of the following members (in brackets: project involvement in percentage of full time employment):
- H. Freistühler (TO) (Leipzig,  30%)  - S. Luckhaus (Leipzig, 15%)  - S. Müller (SAB) (Leipzig,  15%)  - A. DeSimone (Leipzig, 20%)  - D. Kröner (Freiburg, 20%)  - C. Rohde (Freiburg, 20%)  - M. Ohlberger (Freiburg, 20%)  - G. Warnecke (Magdeburg, 25%)  - F. Otto (Bonn, 20%)  - B. Niethammer (F, Bonn, 25%)  - M. Westdickenberg (Bonn, 25%)  - W.-A. Yong (Heidelberg, 25%)  - S. Noelle (Aachen, 20%)  - A. Rendall (Potsdam, 20%)  - F. Finster (Regensburg, 20%)  

Two significant publications for the IHP project are the following:

[1] D. Kröner: Numerical Schemes for Conservation Laws. Wiley-Teubner Series Advances in Numerical Mathematics. Chichester: Wiley. Stuttgart: Teubner. 1997.

[2] H. Friedrich, A. Rendall: The Cauchy problem for the Einstein Equations, Lecture Notes in Phys., 540, Berlin: Springer. 2000, pp. 127--223.

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