Existence and non-uniqueness of stationary states for the Vlasov–Poisson equation on [Formula: see text] subject to attractive background charges

We prove the existence of stationary solutions for the density of an infinitely extended plasma interacting with an arbitrary configuration of background charges. Furthermore, we show that the solution cannot be unique if the total charge of the background is attractive. In this case, infinitely man...

Descripción completa

Detalles Bibliográficos
Autor principal: Winter, Raphael
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2023
Materias:
Original Paper
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10310580/
https://www.ncbi.nlm.nih.gov/pubmed/37398934
http://dx.doi.org/10.1007/s42985-023-00241-3
_version_ 1785066571698274304
author Winter, Raphael
author_facet Winter, Raphael
author_sort Winter, Raphael
collection PubMed
description We prove the existence of stationary solutions for the density of an infinitely extended plasma interacting with an arbitrary configuration of background charges. Furthermore, we show that the solution cannot be unique if the total charge of the background is attractive. In this case, infinitely many different stationary solutions exist. The non-uniqueness can be explained by the presence of trapped particles orbiting the attractive background charge.
format Online
Article
Text
id pubmed-10310580
institution National Center for Biotechnology Information
language English
publishDate 2023
publisher Springer International Publishing
record_format MEDLINE/PubMed
spelling pubmed-103105802023-07-01 Existence and non-uniqueness of stationary states for the Vlasov–Poisson equation on [Formula: see text] subject to attractive background charges Winter, Raphael SN Partial Differ Equ Appl Original Paper We prove the existence of stationary solutions for the density of an infinitely extended plasma interacting with an arbitrary configuration of background charges. Furthermore, we show that the solution cannot be unique if the total charge of the background is attractive. In this case, infinitely many different stationary solutions exist. The non-uniqueness can be explained by the presence of trapped particles orbiting the attractive background charge. Springer International Publishing 2023-06-29 2023 /pmc/articles/PMC10310580/ /pubmed/37398934 http://dx.doi.org/10.1007/s42985-023-00241-3 Text en © The Author(s) 2023 https://creativecommons.org/licenses/by/4.0/Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/ (https://creativecommons.org/licenses/by/4.0/) .
spellingShingle Original Paper
Winter, Raphael
Existence and non-uniqueness of stationary states for the Vlasov–Poisson equation on [Formula: see text] subject to attractive background charges
title Existence and non-uniqueness of stationary states for the Vlasov–Poisson equation on [Formula: see text] subject to attractive background charges
title_full Existence and non-uniqueness of stationary states for the Vlasov–Poisson equation on [Formula: see text] subject to attractive background charges
title_fullStr Existence and non-uniqueness of stationary states for the Vlasov–Poisson equation on [Formula: see text] subject to attractive background charges
title_full_unstemmed Existence and non-uniqueness of stationary states for the Vlasov–Poisson equation on [Formula: see text] subject to attractive background charges
title_short Existence and non-uniqueness of stationary states for the Vlasov–Poisson equation on [Formula: see text] subject to attractive background charges
title_sort existence and non-uniqueness of stationary states for the vlasov–poisson equation on [formula: see text] subject to attractive background charges
topic Original Paper
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10310580/
https://www.ncbi.nlm.nih.gov/pubmed/37398934
http://dx.doi.org/10.1007/s42985-023-00241-3
work_keys_str_mv AT winterraphael existenceandnonuniquenessofstationarystatesforthevlasovpoissonequationonformulaseetextsubjecttoattractivebackgroundcharges

Ejemplares similares