Conditions for the fragmentation of expanding shells due to gravitational instability are discussed. The self-similar analytical solution is compared with the results of 3-dimensional computer simulations for the expansion into homogeneous media. For realistic galactic disks we show that the formation of fragments is influenced by the amount of energy supply from the final number of young stars in an OB association, the value of the sound speed, the stratification and density of the ambient medium, the galactic differential rotation and the gravitational force perpendicular to the galactic plane. The typical size of gravitationally unstable shells is 1 kpc for an ambient gas density n=1 cm^-3. In thick disk galaxies the fragmentation occurs in nearly the whole shell while in thin disks it is restricted to the galactic equator. Unstable fragments may become molecular and trigger the formation of molecular clouds, and finally new star formation. We conclude that in dwarf galaxies the star formation may propagate in all directions turning the system into a star- burst. Contrary to that, the star formation in spiral galaxies propagates only in some directions in a thin strip near the symmetry plane, basically at the tips of the expanding shell.
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