TITLE:
Application of the Method of Non-Classical Approach to Certain Problems of the Theory of Anisotropic Space Plazma in Fluid Description
AUTHORS:
Mahammad A. Nurmammadov, Namiq S. Dzhalilov
KEYWORDS:
ODE, Non-Autonomous and Nonlinear Systems, Anisotropic MHD, Solar Wind Outflow, Singularity, Degenerating
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.9 No.6,
June
10,
2021
ABSTRACT: In this paper, the new well-posed boundary value problem to the system of singular nonlinear differential equations is considered, which describes the stationary radial outflow of anisotropic plasma from the Sun (solar wind). These equations are obtained on the basis of 16-moment MHD (magnetohydrodynamic) transport equations for a collisionless magnetized plasma, which takes into account the temperature anisotropy relative to the direction of the magnetic field and the heat flux carried by the wind. This is a generalization of the classical isotropic Parker model taking into account the effects of anisotropy. In this paper, the equations under study are characterized as a non-autonomous nonlinear system of ordinary differential equations the coefficients in which degenerate and simultaneously have singularities. These equations are related to an unsolved problem in the general theory of ODEs (Ordinary Differential Equations). At first, according to the conditions of the coefficients of the equations, a non-classical boundary value problem is set, and the solvability is established for the same non-autonomous and nonlinear system of equations under consideration. The found analytical solution reconstructs numerical solutions, which are simultaneously automatically established by classical formulation of boundary value problem. Parker’s solutions are also partially included in this obtained class of solutions, which is presented with strictly proves. Further, by means of the methods of “ -regularization” and “fixed point” the theorem of solvability for the considered differential equations is obtained. After constructed nonsingular system equations with well-posed boundary value problem, the analytical solutions are founded. Using the sketch of graph of these solutions their family is established.