Classical solutions of the Vlasov–Poisson equations with external magnetic field in a half-space

We consider the first mixed problem for the Vlasov–Poisson equations with an external magnetic field in a half-space. This problem describes the evolution of the density distributions of ions and electrons in a high temperature plasma with a fixed potential of electric field on a boundary. For arbit...

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Bibliographic Details
Published in:Computational mathematics and mathematical physics 2017-03, Vol.57 (3), p.541-557
Main Authors: Skubachevskii, A. L., Tsuzuki, Y.
Format: Article
Language:English
Subjects:
Boundaries
Cauchy problems
Charged particles
Computational mathematics
Computational Mathematics and Numerical Analysis
Density distribution
Electric fields
Electric potential
Half spaces
High temperature
Magnetic fields
Mathematical analysis
Mathematical models
Mathematics
Mathematics and Statistics
Physics
Plasma
Studies
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Summary:We consider the first mixed problem for the Vlasov–Poisson equations with an external magnetic field in a half-space. This problem describes the evolution of the density distributions of ions and electrons in a high temperature plasma with a fixed potential of electric field on a boundary. For arbitrary potential of electric field and sufficiently large induction of external magnetic field, it is shown that the characteristics of the Vlasov equations do not reach the boundary of the halfspace. It is proved the existence and uniqueness of classical solution with the supports of charged-particle density distributions at some distance from the boundary, if initial density distributions are sufficiently small.
ISSN:0965-5425
1555-6662
DOI:10.1134/S0965542517030137