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

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Abstract

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.
Original languageEnglish
Place of PublicationEindhoven
PublisherTechnische Universiteit Eindhoven
Number of pages19
Publication statusPublished - 2014

Publication series

NameCASA-report
Volume1434
ISSN (Print)0926-4507

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