Analysis of the stationary solutions for initial boundary value problem of nonlocal parabolic equation of plasma physics

G. A. Rudykh

Irkutsk State University, 1, K. Marks St., Irkutsk, 664003

Abstract: The methods of nonlinear functional analysis, we study the properties stationary solutions of initial-boundary value problem for nonlinear nonlocal second order parabolic equation with implicit degeneration. This equation arises in the mathematical simulation of diffusion limited plasma across the magnetic field and its equilibrium configurations in the installation type tokamak. Problem of stabilization of nonstationary solutions to stationary reduced to study of the solvability of nonlinear boundary value problem with nonlocal (integral) operators. Sufficient conditions parameters studied integrodifferential boundary value problem ensure the existence and uniqueness of its classical solutions, for which structurally built area of attraction.

Keywords: nonlocal parabolic and elliptic equation, classical solution, stabilization, the region of attraction, monotone operator, cone, lower and upper solutions, steam fixed point.

UDC: 518.946