ON FORMULATION AND APPROXIMATE SOLUTION OF THE FIRST INTERIOR BOUNDARY-VALUE PROBLEM FOR A SET OF DIFFUSION-TYPE DIFFERENTIAL EQUATIONS WITH NONLINEARITIES

A. Ya. Voronov
VANT. Ser. Metodiki i Programmy Chislennogo Resheniya Zadach Matematicheskoy Fiziki 1986. Вып.1. С. 33-41.

      For a set of differential equations describing properties of partially ionized multicomponent plasma a boundary-value problem is formulated in which, in addition to functions, describing distribution of charged particles of plasma and its self-consistent field in Ω -region, Ω -averaged ionization factor is also considered unknown. In initial equations nonlinear effect which result from Coulomb interaction between charged plasma components, as well as nonlinear elementary process of volume electron-ion recombination are taken into account. Solution of the problem formulated for all unknowns is obtained in form of power series expansion of small parameter. In the specific case, when Ω-region is a circle, solutions of the problem are brought up to numerical results.