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One Approach to the Solution of Problems in Plasma Dynamics
Proceedings of the Steklov Institute of Mathematics ( IF 0.5 ) Pub Date : 2020-03-22 , DOI: 10.1134/s0081543819070095
L. I. Rubina , O. N. Ul’yanov

A system of equations for the motion of an ionized ideal gas is considered. An algorithm for the reduction of this system of nonlinear partial differential equations (PDEs) to systems of ordinary differential equations (ODEs) is presented. It is shown that the independent variable ψ in the systems of ODEs is determined from the relation ψ = t + xf1(ψ) + yf2(ψ) + zf3(ψ) after choosing (setting or finding) the functions fi(ψ), i = 1, 2, 3. These functions are either found from the conditions of the problem posed for the original system of PDEs or are given arbitrarily to obtain a specific system of ODEs. For the problem on the motion of an ionized gas near a body, we write a system of ODEs and discuss the issue of instability, which is observed in a number of cases. We also consider a problem of the motion of flows (particles) in a given direction, which is of significant interest in some areas of physics. We find the functions fi(ψ), i = 1, 2, 3, that provide the motion of a flow of the ionized gas in a given direction and reduce the system of PDEs to a system of ODEs.

中文翻译:

解决等离子体动力学问题的一种方法

考虑了用于电离的理想气体运动的方程组。提出了将非线性偏微分方程组(PDE)简化为常微分方程组(ODE)的算法。结果表明,在选择(设置或发现)函数f i后,ODE系统中的自变量ψ由关系ψ = t + xf 1ψ)+ yf 2ψ)+ zf 3ψ)确定。(ψ),i= 1、2、3。这些功能可以从原始PDE系统提出的问题的条件中找到,也可以任意获得以获得特定的ODE系统。对于电离气体在人体附近运动的问题,我们编写了一个ODE系统,并讨论了在许多情况下观察到的不稳定问题。我们还考虑了流体(粒子)在给定方向上的运动问题,这在某些物理领域引起了极大的兴趣。我们发现函数f iψ),i = 1、2、3,这些函数提供电离气体在给定方向上的运动,并将PDE的系统简化为ODE的系统。
更新日期:2020-03-22
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