Existence and uniqueness of solutions to Liouville's equation and the associated flow for Hamiltonians of bounded variation

B.S. Lith, van, J.H.M. Thije Boonkkamp, ten, W.L. IJzerman, T.W. Tukker

Onderzoeksoutput: Boek/rapportRapportAcademic

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Samenvatting

We prove existence and uniqueness for solutions to Liouville's equation for Hamiltonians of bounded variation. These solutions can be interpreted as the limit of a sequence generated by a series of smooth approximations to the Hamiltonian. This results in a converging sequence of approximations of solutions to Liouville's equation. As an added perk, our method allows us to prove a generalisation of Liouville's theorem for Hamiltonians of bounded variation. Furthermore, we prove there exists a unique flow solution to the Hamilton equations and show how this can be used to construct a solution to Liouville's equation. Key words: partial differential equations, geometrical optics, Liouville's equation, flow.
Originele taal-2Engels
Plaats van productieEindhoven
UitgeverijTechnische Universiteit Eindhoven
Aantal pagina's19
StatusGepubliceerd - 2014

Publicatie series

NaamCASA-report
Volume1434
ISSN van geprinte versie0926-4507

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