Solvability of nonlinear boundary-value problems arising in modeling plasma diffusion across a magnetic field and its equilibrium configurations

G. A. Rudykh, A. V. Sinitsyn

Institute of System Dynamics and Control Theory, Siberian Branch of the Russian Academy of Sciences

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.

UDC: 517.946

Received: 21.08.2002
Revised: 10.11.2003

DOI: 10.4213/mzm2486

 English version: Mathematical Notes, 2005, 77:2, 199–212

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