A mathematical theory of isolated systems in relativistic plasma physics
Autor(a) principal: | |
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Data de Publicação: | 2007 |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | http://hdl.handle.net/1822/6583 |
Resumo: | 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. |
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A mathematical theory of isolated systems in relativistic plasma physicsVlasov-maxwellInitial valueIncoming radiationIsolated solutionsProblem hyperboloidisolated solutioninitial value problembackward hyperboloidoutgoing radiationScience & TechnologyThe 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.Fundação para a Ciência e a Tecnologia (FCT)World Scientific PublishingUniversidade do MinhoCalogero, Simone Carmelo2007-062007-06-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/1822/6583eng"Journal of hyperbolic differential equations". ISSN 0219-8916. 4:2 (June 2007) 267-294.0219-8916http://www.worldscinet.cominfo:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2023-07-21T12:19:05Zoai:repositorium.sdum.uminho.pt:1822/6583Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T19:12:00.237094Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse |
dc.title.none.fl_str_mv |
A mathematical theory of isolated systems in relativistic plasma physics |
title |
A mathematical theory of isolated systems in relativistic plasma physics |
spellingShingle |
A mathematical theory of isolated systems in relativistic plasma physics Calogero, Simone Carmelo Vlasov-maxwell Initial value Incoming radiation Isolated solutions Problem hyperboloid isolated solution initial value problem backward hyperboloid outgoing radiation Science & Technology |
title_short |
A mathematical theory of isolated systems in relativistic plasma physics |
title_full |
A mathematical theory of isolated systems in relativistic plasma physics |
title_fullStr |
A mathematical theory of isolated systems in relativistic plasma physics |
title_full_unstemmed |
A mathematical theory of isolated systems in relativistic plasma physics |
title_sort |
A mathematical theory of isolated systems in relativistic plasma physics |
author |
Calogero, Simone Carmelo |
author_facet |
Calogero, Simone Carmelo |
author_role |
author |
dc.contributor.none.fl_str_mv |
Universidade do Minho |
dc.contributor.author.fl_str_mv |
Calogero, Simone Carmelo |
dc.subject.por.fl_str_mv |
Vlasov-maxwell Initial value Incoming radiation Isolated solutions Problem hyperboloid isolated solution initial value problem backward hyperboloid outgoing radiation Science & Technology |
topic |
Vlasov-maxwell Initial value Incoming radiation Isolated solutions Problem hyperboloid isolated solution initial value problem backward hyperboloid outgoing radiation Science & Technology |
description |
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. |
publishDate |
2007 |
dc.date.none.fl_str_mv |
2007-06 2007-06-01T00:00:00Z |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://hdl.handle.net/1822/6583 |
url |
http://hdl.handle.net/1822/6583 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
"Journal of hyperbolic differential equations". ISSN 0219-8916. 4:2 (June 2007) 267-294. 0219-8916 http://www.worldscinet.com |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
application/pdf |
dc.publisher.none.fl_str_mv |
World Scientific Publishing |
publisher.none.fl_str_mv |
World Scientific Publishing |
dc.source.none.fl_str_mv |
reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação instacron:RCAAP |
instname_str |
Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
instacron_str |
RCAAP |
institution |
RCAAP |
reponame_str |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
collection |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
repository.name.fl_str_mv |
Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação |
repository.mail.fl_str_mv |
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1799132554010296320 |