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Projekt
Minimal Orbits and Hamilton-Jacobi Equations
Antragsteller
Professor Dr. Dietmar Kröner
Fachliche Zuordnung
Mathematik
Förderung
Förderung von 2002 bis 2010
Projektkennung
Deutsche Forschungsgemeinschaft (DFG) - Projektnummer 5469304
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.
DFG-Verfahren
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