Permanent Regimes for the 1D Vlasov--Poisson System with Boundary Conditions

Bostan, Mihaï

doi:10.1137/s0036141002416420

Cited by 9 publications

(8 citation statements)

References 16 publications

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“…One of the key points is to establish a priori estimates. For results on permanent regimes for the Vlasov-Poisson system and Vlasov-Maxwell system the reader can refer to [2,3,9,16,19]. Our main result is the following theorem.…”

Section: Introductionmentioning

confidence: 88%

Stationary solutions for the one-dimensional Nordström–Vlasov system

Bostan¹

2009

Asymptotic Analysis

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Section: Introductionmentioning

confidence: 88%

Stationary solutions for the one-dimensional Nordström–Vlasov system

Bostan¹

2009

Asymptotic Analysis

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“…One of the crucial points is to observe that the change in momentum along characteristics inside a bounded spatial domain can be estimated in term of the L ∞ norm of the electric field. This idea has been already used in [26]. For example, in the classical case we prove that for all characteristic dX ds = P (s) m , dP ds = qE(s, X(s)),…”

Section: Introductionmentioning

confidence: 94%

Weak Solutions for the Vlasov-Poisson Initial-Boundary Value Problem with Bounded Electric Field

Bostan

2007

Chin. Ann. Math. Ser. B

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The aim of this work is to construct weak solutions for the three dimensional Vlasov-Poisson initial-boundary value problem with bounded electric field. The main ingredient consists of estimating the change in momentum along characteristics of regular electric fields inside bounded spatial domains. As direct consequences, the propagation of the momentum moments and the existence of weak solution satisfying the balance of total energy are obtained.

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“…Actually, this result still holds true. In fact, in Reference [23] it was proved that in the classical case the change in momentum along any characteristic is bounded uniformly >0 for some 0. In this case, it can be shown that the change in momentum along any characteristic remains bounded:…”

Section: + (V( P) · N(x))e( P) F (Tmentioning

confidence: 99%

Boundary value problem for theN‐dimensional time periodic Vlasov–Poisson system

Bostan¹

2006

Math Methods in App Sciences

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SUMMARYIn this work, we study the existence of time periodic weak solution for the N -dimensional Vlasov-Poisson system with boundary conditions. We start by constructing time periodic solutions with compact support in momentum and bounded electric field for a regularized system. Then, the a priori estimates follow by computations involving the conservation laws of mass, momentum and energy. One of the key point is to impose a geometric hypothesis on the domain: we suppose that its boundary is strictly star-shaped with respect to some point of the domain. These results apply for both classical or relativistic case and for systems with several species of particles.

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Permanent Regimes for the 1D Vlasov--Poisson System with Boundary Conditions

Abstract: We prove the existence of weak solutions for the Vlasov-Poisson problem with time periodic boundary conditions in one dimension. We consider boundary data with finite charge and current. This analysis is based upon the mild formulation for the regularized Vlasov-Poisson equations.

Cited by 9 publications

References 16 publications

Stationary solutions for the one-dimensional Nordström–Vlasov system

Stationary solutions for the one-dimensional Nordström–Vlasov system

Weak Solutions for the Vlasov-Poisson Initial-Boundary Value Problem with Bounded Electric Field

Boundary value problem for theN‐dimensional time periodic Vlasov–Poisson system

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