Periodic solutions of the 1D Vlasov-Maxwell system with boundary conditions

Bostan, Mihaï; Poupaud, F.

doi:10.1002/1099-1476(20000925)23:14<1195::aid-mma161>3.0.co;2-r

Cited by 8 publications

(10 citation statements)

References 15 publications

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“…Let f ∈ L ∞ be a T periodic function and x ∞ be the periodic solution of the problem (1), given by (8). If f satisfies:…”

Section: Propositionmentioning

confidence: 99%

“…Since x ∞ is periodic, it is sufficient to estimate x ∞ (t) only for t ∈]0, T [. Using (8) we can write:…”

Section: Propositionmentioning

confidence: 99%

“…The periodic Vlasov-Poisson system has been studied in [6] for one space dimension and in [7] for any arbitrary dimension. The Vlasov-Maxwell system in one dimension has been analyzed in [8]. One strong motivation for studying such solutions is the great difficulty to compute them numerically.…”

Section: Introductionmentioning

confidence: 99%

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Numerical study by a controllability method for the calculation of the time-periodic solutions of the Maxwell and Vlasov-Maxwell systems

Bostan¹

2001

ESAIM: M2AN

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Abstract. The topic of this paper is the numerical analysis of time periodic solution for electromagnetic phenomena. The Limit Absorption Method (LAM) which forms the basis of our study is presented. Theoretical results have been proved in the linear finite dimensional case. This method is applied to scattering problems and transport of charged particles.Mathematics Subject Classification. 34A30, 35G60, 35F30.

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“…Let f ∈ L ∞ be a T periodic function and x ∞ be the periodic solution of the problem (1), given by (8). If f satisfies:…”

Section: Propositionmentioning

confidence: 99%

“…Since x ∞ is periodic, it is sufficient to estimate x ∞ (t) only for t ∈]0, T [. Using (8) we can write:…”

Section: Propositionmentioning

confidence: 99%

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Numerical study by a controllability method for the calculation of the time-periodic solutions of the Maxwell and Vlasov-Maxwell systems

Bostan¹

2001

ESAIM: M2AN

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“…The situation is different in 1-D because solutions of Maxwell system can be computed explicitly and the techniques introduced in this paper can be used, see Ref. 11. We now describe precisely the boundary condition which we investigate.…”

Section: Introductionmentioning

confidence: 99%

Periodic Solutions of the Vlasov–poisson System With Boundary Conditions

Bostan

Poupaud

2000

Math. Models Methods Appl. Sci.

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We study the Vlasov-Poisson system with time periodic boundary conditions. For small data we prove existence of weak periodic solutions in any space dimension. In the onedimensional case the result is stronger: we obtain existence of mild solution and uniqueness of this solution when the data are smooth. It is necessary to impose a nonvanishing condition for the incoming velocities in order to control the lifetime of particles in the domain *

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“…The periodic case has been studied as well (see [5], [6], [7]), but existence results are available only under some restrictive hypothesis concerning the velocity support of the boundary incoming particle distribution and the potential data. Basically the above model doesn't handle charge flows with small incoming velocities.…”

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confidence: 99%