Geodesic
Solvability of nonlinear boundary-value problems arising in modeling plasma diffusion across a magnetic field and its equilibrium configurations
Matematičeskie zametki, Tome 77 (2005) no. 2, pp. 219-234

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We study the simplest one-dimensional model of plasma density balance in a tokamak type system, which can be reduced to an initial boundary-value problem for a second-order parabolic equation with implicit degeneration containing nonlocal (integral) operators. The problem of stabilizing nonstationary solutions to stationary ones is reduced to studying the solvability of a nonlinear integro-differential boundary-value problem. We obtain sufficient conditions for the parameters of this boundary-value problem to provide the existence and the uniqueness of a classical stationary solution, and for this solution we obtain the attraction domain by a constructive method. 
@article{MZM_2005_77_2_a5,
     author = {G. A. Rudykh and A. V. Sinitsyn},
     title = {Solvability of nonlinear boundary-value problems arising in modeling plasma diffusion across a magnetic field and its equilibrium configurations},
     journal = {Matemati\v{c}eskie zametki},
     pages = {219--234},
     publisher = {mathdoc},
     volume = {77},
     number = {2},
     year = {2005},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2005_77_2_a5/}
}
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G. A. Rudykh; A. V. Sinitsyn. Solvability of nonlinear boundary-value problems arising in modeling plasma diffusion across a magnetic field and its equilibrium configurations. Matematičeskie zametki, Tome 77 (2005) no. 2, pp. 219-234. http://geodesic.mathdoc.fr/item/MZM_2005_77_2_a5/