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

Nonlocal problems and functional-differential equations: theoretical aspects and applications to mathematical modelling

“…Thus, those solutions are useless from the application viewpoint: if a substantial amount of plasma particles reach the reactor walls, then either the reactor is destroyed or the plasma cools down. Below, we provide the recent result (obtained in [80]) free from the said disadvantage.…”

Stationary solutions of the Vlasov–Poisson system for two-component plasma under an external magnetic field in a half-space

“…Depending on the initial physical models, one distinguishes the Vlasov-Poisson equations, the Vlasov-Maxwell equations, the Vlasov-Einstein equations, the generalized Vlasov equations, and so on. There is an extensive literature on the Vlasov equations (see [1][2][3][4][5][6][7][8][9][10][11][12][13][14] and the references given there).…”

“…Mixed problem for the Vlasov-Poisson equations for high-temperature two-component plasma in a cylindrical domain and in a half-space were studied in [6][7][8][9][10][11]. Note that in [6][7][8][9][10][11] the influence of an external magnetic field on the trajectories of particles was considered. In [4,8] there was constructed a stationary solution for which the charged-particle density distributions were supported in a strictly interior cylinder.…”

A general way to confined stationary Vlasov-Poisson plasma configurations

“…Concerning the confinement problem for a two-component plasma the articles [8,33,34,35,36] provide quantitative estimates for a bounded magnetic field guaranteeing the classical solution to the initial-boundary value problem of (1), (2), (3), (4) to exist and to be located at some distance from the boundary of a half-space and an infinite cylinder.…”

“…Unlike [8,33,34,35,36], the papers [10,11] deal with the confinement problem for a one-component plasma with an external magnetic field, which becomes infinite on a boundary. Equation 2is studied in the whole space R 3 , and the influence of boundary conditions to a solution of equation 2is not considered.…”