• xmlui.mirage2.page-structure.header.title
    • français
    • English
  • Help
  • Login
  • Language 
    • Français
    • English
View Item 
  •   BIRD Home
  • CEREMADE (UMR CNRS 7534)
  • CEREMADE : Publications
  • View Item
  •   BIRD Home
  • CEREMADE (UMR CNRS 7534)
  • CEREMADE : Publications
  • View Item
JavaScript is disabled for your browser. Some features of this site may not work without it.

Browse

BIRDResearch centres & CollectionsBy Issue DateAuthorsTitlesTypeThis CollectionBy Issue DateAuthorsTitlesType

My Account

LoginRegister

Statistics

Most Popular ItemsStatistics by CountryMost Popular Authors
Thumbnail - No thumbnail

On the controllability of the relativistic Vlasov-Maxwell system

Han-Kwan, Daniel; Glass, Olivier (2015), On the controllability of the relativistic Vlasov-Maxwell system, Journal de Mathématiques Pures et Appliquées, 103, 3, p. 695-740. http://dx.doi.org/10.1016/j.matpur.2014.07.007

Type
Article accepté pour publication ou publié
External document link
http://hal.archives-ouvertes.fr/hal-00759279
Date
2015
Journal name
Journal de Mathématiques Pures et Appliquées
Volume
103
Number
3
Publisher
Elsevier
Pages
695-740
Publication identifier
http://dx.doi.org/10.1016/j.matpur.2014.07.007
Metadata
Show full item record
Author(s)
Han-Kwan, Daniel
Glass, Olivier
Abstract (EN)
In this paper, we study the controllability of the two-dimensional relativistic Vlasov-Maxwell system in a torus, by means of an interior control. We give two types of results. With the geometric control condition on the control set, we prove the local exact controllability of the system in large time. Our proof in this case is based on the return method, on some results on the control of the Maxwell equations, and on a suitable approximation scheme to solve the non-linear Vlasov-Maxwell system on the torus with an absorption procedure. Without geometric control condition, but assuming that a strip of the torus is contained in the control set and under certain additional conditions on the initial data, we establish a controllability result on the distribution function only, also in large time. Here, we need some additional arguments based on the asymptotics of the Vlasov-Maxwell system with large speed of light and on our previous results concerning the controllability of the Vlasov-Poisson system with an external magnetic field [14].
Subjects / Keywords
Vlasov–Poisson system; Controllability

Related items

Showing items related by title and author.

  • Thumbnail
    On the controllability of the Vlasov-Poisson system in the presence of external force fields 
    Han-Kwan, Daniel; Glass, Olivier (2012) Article accepté pour publication ou publié
  • Thumbnail
    The Vlasov-Navier-Stokes system in a 2D pipe: existence and stability of regular equilibria 
    Moussa, Ayman; Glass, Olivier; Han-Kwan, Daniel (2018) Article accepté pour publication ou publié
  • Thumbnail
    On the controllability of the Vlasov–Poisson system 
    Glass, Olivier (2003) Article accepté pour publication ou publié
  • Thumbnail
    A Remark on the Controllability of a System of Conservation Laws in the Context of Entropy Solutions 
    Glass, Olivier (2010) Chapitre d'ouvrage
  • Thumbnail
    An addendum to a J.M. Coron theorem concerning the controllability of the Euler system for 2D incompressible inviscid fluids 
    Glass, Olivier (2001) Article accepté pour publication ou publié
Dauphine PSL Bibliothèque logo
Place du Maréchal de Lattre de Tassigny 75775 Paris Cedex 16
Phone: 01 44 05 40 94
Contact
Dauphine PSL logoEQUIS logoCreative Commons logo