Premium
Boundary value problem for the N ‐dimensional time periodic Vlasov–Poisson system
Author(s) -
Bostan M.
Publication year - 2006
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.752
Subject(s) - bounded function , mathematics , boundary value problem , momentum (technical analysis) , mathematical analysis , conservation law , domain (mathematical analysis) , boundary (topology) , initial value problem , energy–momentum relation , a priori and a posteriori , classical mechanics , physics , philosophy , finance , epistemology , economics
In 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. Copyright © 2006 John Wiley & Sons, Ltd.