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- W797864418 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." @default.
- W797864418 created "2016-06-24" @default.
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- W797864418 date "2014-01-01" @default.
- W797864418 modified "2023-09-23" @default.
- W797864418 title "Existence and uniqueness of solutions to Liouville's equation and the associated flow for Hamiltonians of bounded variation" @default.
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