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TitleA mathematical theory of isolated systems in relativistic plasma physics
Author(s)Calogero, Simone Carmelo
Initial value
Incoming radiation
Isolated solutions
Problem hyperboloid
isolated solution
initial value problem
backward hyperboloid
outgoing radiation
Issue dateJun-2007
PublisherWorld Scientific Publishing
JournalJournal of hyperbolic differential equations
Citation"Journal of hyperbolic differential equations". ISSN 0219-8916. 4:2 (June 2007) 267-294.
Abstract(s)The existence and the properties of isolated solutions to the relativistic Vlasov-Maxwell system with initial data on the backward hyperboloid $t=-\sqrt{1+|x|^2}$ are investigated. Isolated solutions of Vlasov-Maxwell can be defined by the condition that the particle density is compactly supported on the initial hyperboloid and by imposing the absence of incoming radiation on the electromagnetic field. Various consequences of the mass-energy conservation laws are derived by assuming the existence of smooth isolated solutions which match the inital data. In particular, it is shown that the mass-energy of isolated solutions on the backward hyperboloids and on the surfaces of constant proper time are preserved and equal, while the mass-energy on the forward hyperboloids is non-increasing and uniformly bounded by the mass-energy on the initial hyperboloid. Moreover the global existence and uniqueness of classical solutions in the future of the initial surface is established for the one dimensional version of the system.
Publisher version
AccessOpen access
Appears in Collections:Offmath - Artigos (Papers)

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