One-dimensional compression of bounded volumes of a self-gravitating gas

Unsteady plane and spherically-symmetric self-gravitating gas flows are analytically and numerically studied. It is assumed that the gas is enclosed in a plane layer of finite thickness or in a bounded spherical volume. Two characteristic compression patterns are established, namely, a quasiperiodic regime in which gravitational equilibrium is attained and a fast compression regime with a many orders increase in the density. The quasiperiodic regime is realized when the layer thickness is fairly small as compared with the Jeans length. The fast compression occurs when the layer thickness is greater than the Jeans length.