In this paper, the gravitational field equations for static spherically symmetric perfect fluid models with a polytropic equation of state, p = kρ1+1/n, are recast into two complementary 3-dimensional regular systems of ordinary differential equations on compact state spaces. The systems are analyzed numerically and qualitatively, using the theory of dynamical systems. Certain key solutions are...

We discuss stability of spherically symmetric static solutions in Newtonian limit of Jordan, Brans-Dicke field equations. The behavior of the stable equilibrium solutions for the spherically symmetric configurations considered here, it emerges that the more compact a model is, the more stable it is. Moreover, linear stability analysis shows the existence of stable configurations for any polytro...

This paper deals with the global existence and blow-up of a non-Newtonian polytropic filtration equation with multiple nonlinearities. We obtain necessary and sufficient conditions on the global existence of all positive solutions by constructing super solutions and sub solutions. AMS Subject Classifications: 35K50, 35K55, 35K65.

Emission line profiles of tracer molecule H2CO 140 GHz transition from gravitational core collapsing clouds in the dynamic process of forming protostars are calculated, using a simple ray-tracing radiative transfer model. Three self-similar dynamic insideout core collapse models – the conventional polytropic model, the empirical hybrid model and the isothermal model – for star-forming molecular...