Geodesic
Plasma confinement in the field of a magnetic dipole
Matematičeskie zametki SVFU, Tome 25 (2018) no. 2, pp. 97-108 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider a particular case of the earlier studied by the author second order degenerate differential operator with the same assumptions and designations. We focus on the study of the effects associated with the “strong” degeneration. The problem is solved to be used in further researches of formally conjugated (coupled transposition operation) equation and also for obtaining some theorems of existence and uniqueness for generalized solutions of formally conjugated equations from the proved theorem. The use of the following results is reduced to the operator equations in the simplest case. We study existence and uniqueness of the generalized solution of the first boundary value problem for the given equation using the operator theory and obtain the generalized solution to the equation in the case connected with “strong” degeneration. The results will be used in the future for research of equations with model operators which arise in mathematical modeling of various physical processes.
Keywords: plasma, magnetic dipole, Grad–Shafranov equation. 
@article{SVFU_2018_25_2_a8,
     author = {G. F. Krymsky and Yu. A. Romashchenko and E. P. Sharin},
     title = {Plasma confinement in the field of a magnetic dipole},
     journal = {Matemati\v{c}eskie zametki SVFU},
     pages = {97--108},
     year = {2018},
     volume = {25},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SVFU_2018_25_2_a8/}
}
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G. F. Krymsky; Yu. A. Romashchenko; E. P. Sharin. Plasma confinement in the field of a magnetic dipole. Matematičeskie zametki SVFU, Tome 25 (2018) no. 2, pp. 97-108. http://geodesic.mathdoc.fr/item/SVFU_2018_25_2_a8/