Application of the Cole-Hopf transformation for finding the analytical solutions of the dynamics of a gravitating system of spherical gas-dust cloud

Volume 12, Issue 12, pp 846--855 http://dx.doi.org/10.22436/jnsa.012.12.06

Publication Date: August 07, 2019 Submission Date: April 20, 2019 Revision Date: May 23, 2019 Accteptance Date: June 02, 2019

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Authors

Mohammed Abobaker - Department of Theoretical Mechanics, Institute of Applied Mathematics and Mechanics, St. Petersburg Polytechnic University, Russia.

Abstract

In this paper, we present a simple model for the dynamics of one dimensional of a self-gravitating spherical symmetrical gas-dust cloud. We consider two special initial conditions for density and velocity. We take an analytical Cole-Hopf transformation method to study the dynamics of a gravitating system of a gas-dust cloud. The technique is employed to simplify the equations of dynamics, and after that, we applied the method of characteristics to reduce partial differential equations to a system of entirely solvable ordinary differential equations. The obtained results in this study are presented in graphics.

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Keywords

• Hydrodynamics
• non-linear PDE
• Cole-Hopf method
• gravitating system gas-dust cloud

MSC

•  35Q85
•  85A05

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