Stability analysis of a Vlasov-wave system describing particles interacting with their environment
type: Item
instance of: scholarly article
title: Stability analysis of a Vlasov-wave system describing particles interacting with their environment
zbMATH Open document ID: 1390.82052
author: Peng Zhang
published in: Journal of Differential Equations
publication date: 2018-04-04T00:00:00Z
full work available at URL: Stability VW July.pdf
review text: The considered Vlasov-Wave type kinetic equation which describes the interaction between a large set of particles and their environment has been introduced by the authors in a previous paper: [SIAM J. Math. Anal. 48, No. 6, 3984--4020 (2016; Zbl 1357.82063)]. In the present article, the existence of stationary solutions and their stability are investigated. An infinite family of stationary solutions is obtained by minimizing some energy functional. Actually one concentrates on the critical points of the Casimir-energy function under a mass constraint. Further the dynamical stability is studied.
reviewed by: Claudia Simionescu-Badea
Mathematics Subject Classification ID: 82C70
Mathematics Subject Classification ID: 70F45
Mathematics Subject Classification ID: 37K05
Mathematics Subject Classification ID: 74A25
Mathematics Subject Classification ID: 35Q83
Mathematics Subject Classification ID: 60K37
Mathematics Subject Classification ID: 82C22
zbMATH DE Number: 6855896
zbMATH Keywords: Vlasov-like equation
zbMATH Keywords: interacting particles
zbMATH Keywords: dynamical stability
zbMATH Keywords: inelastic Lorentz gas
MaRDI profile type: Publication
OpenAlex ID: W2777048570
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Wikidata QID: Q130196661
DOI: 10.1016/J.JDE.2018.02.008
description: scientific article; zbMATH DE number 6855896