GRK 243:  Nonlinear Differential Equations: Modelling, Theory, Numerics, Visualisation

• Subject Area: Mathematics
• Term: from 1996 to 2004
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 271151

Non-linear differential equations play a fundamental role in themodelling of physical, chemical, and ecological processes and in theunderstanding of fundamental mathematical problems. The type and form of the differential equations which appear in the modelling of the above mentioned processes are often the same or similar. Modelling, theory and visualisation of such processes are tackled within the group using interdisciplinary techniques. Theoretical investigation of existence, uniqueness and the formation of singularities can give indications of an adequate or inadequate model. On the other hand, numerical simulations of theoretically justified models can give the theorist a graphical representation of the process, and so lead to new insights into the problem and possible directions that may be taken in analysing the model. From a practical point of view, a theoretically numerical simulation can often replace expensiveexperiments. From a practical point of view, a theoreticallygrounded numerical simulation can often replace expensive experiments.A doctoral student in the graduate programme should obtain a solidtraining in theoretical models of physical processes, theoretical andnumerical analysis of the model, and visualisation of the resultsprocured through this analysis. The group receives regular visits fromexperts in their fields, who hold short courses during their stay.Travel expenses are available to members of the group who wish to visit other groups or persons for research purposes.

• DFG Programme: Research Training Groups
• Applicant Institution: Albert-Ludwigs-Universität Freiburg
• Participating Institution: Institut für Sonnenphysik (KIS)
• Spokesperson: Professor Dr. Dietmar Kröner
• Participating Researchers: Professor Dr. Victor Bangert; Professor Dr. Klaus Werner Benz; Professor Dr. Jochum van der Bij; Privatdozent Dr. Peter Dold; Professor Dr. Gerhard Dziuk; Professor Dr. Ernst Eberlein; Professor Dr. Josef Honerkamp (†); Professor Dr. Jan Gerrit Korvink; Professor Dr. Ernst Kuwert; Professor Dr. Michael Ruzicka; Professor Dr. Hartmann Römer; Professor Dr. Ludger Rüschendorf; Professor Dr. Michael Stix; Professor Dr. Jens Timmer