The gravitational instability of expanding shells triggering the formation of clouds and stars is analyzed. Disks with different scale-heights, ambient and shell velocity dispersions, mid-plane densities, rotation rates and shear rates are explored with three dimensional numerical simulations in the thin shell approximation. Three conditions for the shell collapse are specified: the first is that it happens before a significant blow-out, the second requires that the shell collapses before it is distorted by Coriolis forces and shear, and the third requires that the internal pressure in the accumulated gas is small and the fragmentation is achieved within the expansion time. The gas-rich and slowly rotating galaxies are the best sites of the triggered star formation, concluding that its importance has been much larger at the times of galaxy formation compared to the present epoch.
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