Geodesic
Initial-boundary value problems for the Vlasov--Poisson equations in a~half-space
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Function theory and equations of mathematical physics, Tome 283 (2013), pp. 204-232

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We consider initial-boundary value problems for the Vlasov–Poisson equations in a half-space that describe evolution of densities for ions and electrons in a rarefied plasma. For sufficiently small initial densities with compact supports and large strength of an external magnetic field, we prove the existence and uniqueness of classical solutions for initial-boundary value problems with different boundary conditions for the electric potential: the Dirichlet conditions, the Neumann conditions, and nonlocal conditions. 
@article{TM_2013_283_a13,
     author = {A. L. Skubachevskii},
     title = {Initial-boundary value problems for the {Vlasov--Poisson} equations in a~half-space},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {204--232},
     publisher = {mathdoc},
     volume = {283},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2013_283_a13/}
}
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A. L. Skubachevskii. Initial-boundary value problems for the Vlasov--Poisson equations in a~half-space. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Function theory and equations of mathematical physics, Tome 283 (2013), pp. 204-232. http://geodesic.mathdoc.fr/item/TM_2013_283_a13/