Abstract
The star formation triggered in dense walls of expanding shells is discussed. The fragmentation process is studied using the linear and non-linear perturbation theory. The influence of the energy input, the ISM distribution, and the speed of sound is examined analytically and by numerical simulations. We formulate the condition for the gravitational fragmentation of expanding shells: if the total surface density of the disc is higher than a certain critical value, shells are unstable. This value depends on the energy of the shell and the sound speed in the ISM. As an example the formation of OB associations near the Sun is discussed. We trace their orbits in the Milky Way to see where they have been born: 10-12 Myr ago progenitors of the Scorpius-Centaurus OB associations and the Orion OB association resided together within a sheet-like region elongated in the l = 20^o-200^o direction, showing that the local OB associations may be formed as fragments of an expanding supershell.
