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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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

Vingerafdruk

Liouville Equation
Bounded variation
Existence and Uniqueness of Solutions
Smooth Approximation
Liouville's theorem
Geometrical Optics
Existence and Uniqueness
Partial differential equation
Series
Approximation

Citeer dit

Lith, van, B. S., Thije Boonkkamp, ten, J. H. M., IJzerman, W. L., & Tukker, T. W. (2014). Existence and uniqueness of solutions to Liouville's equation and the associated flow for Hamiltonians of bounded variation. (CASA-report; Vol. 1434). Eindhoven: Technische Universiteit Eindhoven.
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Existence and uniqueness of solutions to Liouville's equation and the associated flow for Hamiltonians of bounded variation. / Lith, van, B.S.; Thije Boonkkamp, ten, J.H.M.; IJzerman, W.L.; Tukker, T.W.

Eindhoven : Technische Universiteit Eindhoven, 2014. 19 blz. (CASA-report; Vol. 1434).

Onderzoeksoutput: Boek/rapportRapportAcademic

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