Abstract
The Jeans instability is an astrophysical idea associated with the collapse of a fluctuated infinite homogeneous self-gravitating gas. If a fluctuation ideally takes the form of a plane wave, then the growth of the wavelength is a factor of the instability. As a model we consider a system of equations describing the one-dimensional periodic motion of a self-gravitating viscous gas. Concerning the model system we study the structure of the whole stationary solutions, the asymptotic behavior of solutions, and the nonlinear stability of stationary solutions. The Jeans instability is closely related with bifurcation of solutions in the stationary problem of the model system.
