Addendum: Boundary value problems for the Vlasov-Maxwell equation in one dimension
type: Item
instance of: scholarly article
title: Addendum: Boundary value problems for the Vlasov-Maxwell equation in one dimension
zbMATH Open document ID: 0571.35090
DOI: 10.1016/0022-247X(81)90194-3
author: Jeffery Cooper
author: Alexander J. Klimas
published in: Journal of Mathematical Analysis and Applications
publication date: 1981-01-01T00:00:00Z
review text: This paper is an addendum to our paper [ibid. 75, 306-329 (1980; Zbl 0454.35075)] in which we discussed the existence and uniqueness of solutions of the initial value problem for the Vlasov-Maxwell system of equations in one space dimension. These equations are used to model longitudinal oscillations of a plasma when the ions are considered a stable background. We shall study a boundary value problem for periodic solutions of the Vlasov-Poisson system and determine how its solutions are related to the solutions of the Vlasov-Maxwell system. Our results will be valid for generalized solutions of either the Vlasov-Poisson system or the Vlasov- Maxwell system.
Mathematics Subject Classification ID: 35Q99
Mathematics Subject Classification ID: 78A25
Mathematics Subject Classification ID: 35A05
Mathematics Subject Classification ID: 35B10
Mathematics Subject Classification ID: 35D05
zbMATH DE Number: 3910936
zbMATH Keywords: boundary value problems
zbMATH Keywords: Vlasov-Maxwell equation
zbMATH Keywords: global existence in time
zbMATH Keywords: uniqueness of solutions
zbMATH Keywords: Cauchy problem
zbMATH Keywords: longitudinal oscillations
zbMATH Keywords: plasma
zbMATH Keywords: generalized solutions
zbMATH Keywords: Vlasov-Poisson system
MaRDI profile type: Publication
cites work: Boundary value problems for the Vlasov-Maxwell equation in one dimension
cites work: The Cauchy problem for the kinetic equation of plasma
full work available at URL: 0022-247x(81)90194-3
OpenAlex ID: W2055910607
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description: scientific article; zbMATH DE number 3910936