TY - BOOK

T1 - Existence and uniqueness of solutions to Liouville's equation and the associated flow for Hamiltonians of bounded variation

AU - Lith, van, B.S.

AU - Thije Boonkkamp, ten, J.H.M.

AU - IJzerman, W.L.

AU - Tukker, T.W.

PY - 2014

Y1 - 2014

N2 - 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.

AB - 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.

M3 - Report

T3 - CASA-report

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

PB - Technische Universiteit Eindhoven

CY - Eindhoven

ER -