{"title":"有边界层的 Vlasov-Poisson 系统的近似解","authors":"","doi":"10.1016/j.physd.2024.134320","DOIUrl":null,"url":null,"abstract":"<div><p>We construct the approximate solutions to the Vlasov–Poisson system in a half-space, which arises in the study of the quasi-neutral limit problem in the presence of a sharp boundary layer, referred as to the plasma sheath in the context of plasma physics. The quasi-neutrality is an important characteristic of plasmas and its scale is characterized by a small parameter, called the Debye length. We present the approximate equations obtained by a formal expansion in the parameter and study the properties of the approximate solutions. Moreover, we present numerical experiments demonstrating that the approximate solutions converge to those of the Vlasov–Poisson system as the parameter goes to zero.</p></div>","PeriodicalId":20050,"journal":{"name":"Physica D: Nonlinear Phenomena","volume":null,"pages":null},"PeriodicalIF":2.7000,"publicationDate":"2024-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Approximate solutions for the Vlasov–Poisson system with boundary layers\",\"authors\":\"\",\"doi\":\"10.1016/j.physd.2024.134320\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We construct the approximate solutions to the Vlasov–Poisson system in a half-space, which arises in the study of the quasi-neutral limit problem in the presence of a sharp boundary layer, referred as to the plasma sheath in the context of plasma physics. The quasi-neutrality is an important characteristic of plasmas and its scale is characterized by a small parameter, called the Debye length. We present the approximate equations obtained by a formal expansion in the parameter and study the properties of the approximate solutions. Moreover, we present numerical experiments demonstrating that the approximate solutions converge to those of the Vlasov–Poisson system as the parameter goes to zero.</p></div>\",\"PeriodicalId\":20050,\"journal\":{\"name\":\"Physica D: Nonlinear Phenomena\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":2.7000,\"publicationDate\":\"2024-08-13\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Physica D: Nonlinear Phenomena\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0167278924002719\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Physica D: Nonlinear Phenomena","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0167278924002719","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
Approximate solutions for the Vlasov–Poisson system with boundary layers
We construct the approximate solutions to the Vlasov–Poisson system in a half-space, which arises in the study of the quasi-neutral limit problem in the presence of a sharp boundary layer, referred as to the plasma sheath in the context of plasma physics. The quasi-neutrality is an important characteristic of plasmas and its scale is characterized by a small parameter, called the Debye length. We present the approximate equations obtained by a formal expansion in the parameter and study the properties of the approximate solutions. Moreover, we present numerical experiments demonstrating that the approximate solutions converge to those of the Vlasov–Poisson system as the parameter goes to zero.
期刊介绍:
Physica D (Nonlinear Phenomena) publishes research and review articles reporting on experimental and theoretical works, techniques and ideas that advance the understanding of nonlinear phenomena. Topics encompass wave motion in physical, chemical and biological systems; physical or biological phenomena governed by nonlinear field equations, including hydrodynamics and turbulence; pattern formation and cooperative phenomena; instability, bifurcations, chaos, and space-time disorder; integrable/Hamiltonian systems; asymptotic analysis and, more generally, mathematical methods for nonlinear systems.