Contractive probability metrics and asymptotic behavior of dissipative kinetic equations

The present notes are intended to present a detailed review of the existing results in dissipative kinetic theory which make use of the contraction properties of two main families of probability metrics: optimal mass transport and Fourier-based metrics. The first part of the notes is devoted to a se...

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Detalles Bibliográficos
Autores: Carrillo de la Plata, José Antonio, Toscani, Giuseppe
Tipo de recurso: artículo
Fecha de publicación:2007
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:44032
Acceso en línea:https://ddd.uab.cat/record/44032
Access Level:acceso abierto
Palabra clave:Probabilitats, Mesures de
Equacions diferencials parcials
Maxwell-boltzmann, Llei de distribució de
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spelling Contractive probability metrics and asymptotic behavior of dissipative kinetic equationsCarrillo de la Plata, José AntonioToscani, GiuseppeProbabilitats, Mesures deEquacions diferencials parcialsMaxwell-boltzmann, Llei de distribució deThe present notes are intended to present a detailed review of the existing results in dissipative kinetic theory which make use of the contraction properties of two main families of probability metrics: optimal mass transport and Fourier-based metrics. The first part of the notes is devoted to a self-consistent summary and presentation of the properties of both probability metrics, including new aspects on the relationships between them and other metrics of wide use in probability theory. These results are of independent interest with potential use in other contexts in Partial Differential Equations and Probability Theory. The second part of the notes makes a different presentation of the asymptotic behavior of Inelastic Maxwell Models than the one presented in the literature and it shows a new example of application: particle's bath heating. We show how starting from the contraction properties in probability metrics, one can deduce the existence, uniqueness and asymptotic stability in classical spaces. A global strategy with this aim is set up and applied in two dissipative models.Centre de Recerca MatemàticaCentre de Recerca Matemàtica, 730 22007-01-0120072007-01-01Articlehttp://purl.org/coar/resource_type/c_6501AOhttp://purl.org/coar/version/c_b1a7d7d4d402bcceinfo:eu-repo/semantics/articleapplication/pdfhttps://ddd.uab.cat/record/44032reponame:Dipòsit Digital de Documents de la UABinstname:Universitat Autònoma de BarcelonaInglésengopen accesshttp://purl.org/coar/access_right/c_abf2Aquest document està subjecte a una llicència d'ús Creative Commons. Es permet la reproducció total o parcial, la distribució, i la comunicació pública de l'obra, sempre que no sigui amb finalitats comercials, i sempre que es reconegui l'autoria de l'obra original. No es permet la creació d'obres derivades.https://creativecommons.org/licenses/by-nc-nd/2.5/info:eu-repo/semantics/openAccessoai:ddd.uab.cat:440322026-06-06T12:50:31Z
dc.title.none.fl_str_mv Contractive probability metrics and asymptotic behavior of dissipative kinetic equations
title Contractive probability metrics and asymptotic behavior of dissipative kinetic equations
spellingShingle Contractive probability metrics and asymptotic behavior of dissipative kinetic equations
Carrillo de la Plata, José Antonio
Probabilitats, Mesures de
Equacions diferencials parcials
Maxwell-boltzmann, Llei de distribució de
title_short Contractive probability metrics and asymptotic behavior of dissipative kinetic equations
title_full Contractive probability metrics and asymptotic behavior of dissipative kinetic equations
title_fullStr Contractive probability metrics and asymptotic behavior of dissipative kinetic equations
title_full_unstemmed Contractive probability metrics and asymptotic behavior of dissipative kinetic equations
title_sort Contractive probability metrics and asymptotic behavior of dissipative kinetic equations
dc.creator.none.fl_str_mv Carrillo de la Plata, José Antonio
Toscani, Giuseppe
author Carrillo de la Plata, José Antonio
author_facet Carrillo de la Plata, José Antonio
Toscani, Giuseppe
author_role author
author2 Toscani, Giuseppe
author2_role author
dc.contributor.none.fl_str_mv Centre de Recerca Matemàtica, 730
dc.subject.none.fl_str_mv Probabilitats, Mesures de
Equacions diferencials parcials
Maxwell-boltzmann, Llei de distribució de
topic Probabilitats, Mesures de
Equacions diferencials parcials
Maxwell-boltzmann, Llei de distribució de
description The present notes are intended to present a detailed review of the existing results in dissipative kinetic theory which make use of the contraction properties of two main families of probability metrics: optimal mass transport and Fourier-based metrics. The first part of the notes is devoted to a self-consistent summary and presentation of the properties of both probability metrics, including new aspects on the relationships between them and other metrics of wide use in probability theory. These results are of independent interest with potential use in other contexts in Partial Differential Equations and Probability Theory. The second part of the notes makes a different presentation of the asymptotic behavior of Inelastic Maxwell Models than the one presented in the literature and it shows a new example of application: particle's bath heating. We show how starting from the contraction properties in probability metrics, one can deduce the existence, uniqueness and asymptotic stability in classical spaces. A global strategy with this aim is set up and applied in two dissipative models.
publishDate 2007
dc.date.none.fl_str_mv 2
2007-01-01
2007
2007-01-01
dc.type.none.fl_str_mv Article
http://purl.org/coar/resource_type/c_6501
AO
http://purl.org/coar/version/c_b1a7d7d4d402bcce
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://ddd.uab.cat/record/44032
url https://ddd.uab.cat/record/44032
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
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dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2
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eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Centre de Recerca Matemàtica
publisher.none.fl_str_mv Centre de Recerca Matemàtica
dc.source.none.fl_str_mv reponame:Dipòsit Digital de Documents de la UAB
instname:Universitat Autònoma de Barcelona
instname_str Universitat Autònoma de Barcelona
reponame_str Dipòsit Digital de Documents de la UAB
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