TITLE:
The Case of Nonzero Initial Conditions in the Evolution of the Charge Density Distribution Function for a Spherically Symmetric System
AUTHORS:
Boris I. Sadovnikov, Alex A. Zhavoronkov
KEYWORDS:
Cauchy Problem, Nonzero Initial Conditions, Charge Density Distribution
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.2 No.7,
June
13,
2014
ABSTRACT:
We explored the Cauchy problem for the evolution of the charge density
distribution function for a spherically symmetric system with nonzero initial
conditions. In our model, the evolution of the charge density distribution
function is simulated for the case of a non-uniform charged sphere. The initial
speed of the system is nonzero. The solution breaks down into two components:
the first one describes the system’s motion as a whole and the second describes
the process of the evolution of the charge density function under the influence
of its own electric field in the center-of-mass system. In this paper we
considered the characteristic features of the implementation of a difference
scheme for numerical simulation. We also illustrate the process of “scattering”
of a moving charged system under the influence of its own electric field on the
basis of the solution of the Cauchy problem for vector functions of the
electric field and vector velocity field of a charged medium.