Singular solutions of the Vlasov-Maxwell system on a half line
type: Item
instance of: scholarly article
title: Singular solutions of the Vlasov-Maxwell system on a half line
zbMATH Open document ID: 0840.76097
DOI: 10.1007/BF00382888
author: Yan Guo
published in: Archive for Rational Mechanics and Analysis
publication date: 1996-01-10T00:00:00Z
review text: The Vlasov-Maxwell system describes the time evolution of a collisionless, hot plasma. The electrons or ions are given by a phase-space density which satisfies a first order partial differential equation, the Vlasov equation, and this equation is self-consistently coupled to the Maxwell equations for the electromagnetic field. In order to model physically realistic situations for confined plasmas, the inclusion of boundary conditions for the particles and the fields is very important. In a previous paper the author proved global existence of weak solutions to the corresponding initial-boundary value problem in the three-dimensional case. In the paper under review, he investigates the regularity of solutions for a plasma on a half line; in such a one-dimensional situation the system reduces to the Vlasov-Poisson system. The boundary conditions considered include purely specular reflection as well as partial absorption of the particles, and the detailed and comprehensive analysis reveals that the regularity or singularity of the solutions depends strongly on the type of boundary conditions and on whether the plasma is monocharged, contains differently charged particles, or is neutral. For example, in the case of partial absorption and two oppositely charged particle species, examples show that singularities appear at the boundary and propagate along characteristics into the plasma.
reviewed by: Gerhard Rein
Mathematics Subject Classification ID: 76X05
Mathematics Subject Classification ID: 35L67
Mathematics Subject Classification ID: 82D10
zbMATH DE Number: 832138
zbMATH Keywords: boundary conditions
zbMATH Keywords: regularity of solutions
zbMATH Keywords: Vlasov-Poisson system
zbMATH Keywords: purely specular reflection
zbMATH Keywords: partial absorption
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf00382888
OpenAlex ID: W1986868965
description: scientific article; zbMATH DE number 832138