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 publiéExternal document link
http://hal.archives-ouvertes.fr/hal-00759279Date
2015Journal name
Journal de Mathématiques Pures et AppliquéesVolume
103Number
3Publisher
Elsevier
Pages
695-740
Publication identifier
Metadata
Show full item recordAbstract (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; ControllabilityRelated items
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