Geodesic
Application of the Cole-Hopf transformation for finding the analytical solutions of the dynamics of a gravitating system of spherical gas-dust cloud
Abobaker, Mohammed 1
1 Department of Theoretical Mechanics, Institute of Applied Mathematics and Mechanics, St. Petersburg Polytechnic University, Russia
Journal of nonlinear sciences and its applications, Tome 12 (2019) no. 12, p. 846-855.

Voir la notice de l'article provenant de la source International Scientific Research Publications

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.
DOI : 10.22436/jnsa.012.12.06
Classification : 35Q85, 85A05
Keywords: Hydrodynamics, non-linear PDE, Cole-Hopf method, gravitating system gas-dust cloud

Abobaker, Mohammed  1

1 Department of Theoretical Mechanics, Institute of Applied Mathematics and Mechanics, St. Petersburg Polytechnic University, Russia 
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Abobaker, Mohammed . Application of the Cole-Hopf transformation for finding the analytical solutions of the dynamics of a gravitating system of spherical gas-dust cloud. Journal of nonlinear sciences and its applications, Tome 12 (2019) no. 12, p. 846-855. doi : 10.22436/jnsa.012.12.06. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.012.12.06/

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