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| | Project B2: Minimal Orbits and Hamilton-Jacobi Equations | | | |
We shall develop the numerical analysis of certain aspects
of periodic positive-definite Lagrangian systems (e.g. of
geodesic flows on the n-torus): globally action-minimising
semi-orbits (geodesic rays) and weak KAM tori, that provide
some insight in the behaviour of the Euler flow of the action functional.
Adapting a standard approach of optimal control theory to this particular
situation, we obtain periodic (in time and space) boundary value problems
for certain Hamilton-Jacobi-Bellman (HJB) equations or alternatively
hyperbolic systems of conservation laws. The numerical schemes we
consider approximate solutions of these PDE problems in order
to construct weak KAM tori and associated minimal semi-orbits.
We shall analyse the schemes with respect to existence of
discrete solutions, stability, convergence, error estimates.
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| | Project leader | | | |
Prof. Dr. Dietmar Kröner
Institut für Angewandte Mathematik
Albert-Ludwigs-Universität
Hermann-Herder-Str. 10
D-79104 Freiburg im Breisgau
Germany
Tel. +49 761 203-5637
Fax +49 761 203-5632
dietmar@mathematik.uni-freiburg.de
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