Solvability of nonlinear boundary-value problems arising in modeling plasma diffusion across a magnetic field and its equilibrium configurations |
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Authors: | G. A. Rudykh A. V. Sinitsyn |
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Affiliation: | (1) Institute for System Dynamics and Control Theory, Siberian Division of the Russian Academy of Sciences, Irkutsk |
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Abstract: | 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.Translated from Matematicheskie Zametki, vol. 77, no. 2, 2005, pp. 219–234.Original Russian Text Copyright © 2005 by G. A. Rudykh, A. V. Sinitsyn.This revised version was published online in April 2005 with a corrected issue number. |
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Keywords: | initial boundary-value problem second-order parabolic equation existence and uniqueness theorems stationary solution plasma diffusion tokamak |
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