Geodesic
Classical solutions of the Vlasov–Poisson equations with external magnetic field in a half-space
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 57 (2017) no. 3, pp. 536-552

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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. 
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     author = {A. L. Skubachevskii and Y. Tsuzuki},
     title = {Classical solutions of the {Vlasov{\textendash}Poisson} equations with external magnetic field in a half-space},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
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     publisher = {mathdoc},
     volume = {57},
     number = {3},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2017_57_3_a12/}
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A. L. Skubachevskii; Y. Tsuzuki. Classical solutions of the Vlasov–Poisson equations with external magnetic field in a half-space. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 57 (2017) no. 3, pp. 536-552. http://geodesic.mathdoc.fr/item/ZVMMF_2017_57_3_a12/