Abstract
The asymptotic wave approach has been used to study the gravitational collapse of self-gravitating gaseous systems. In the case of sonic waves it is shown that macroscopic phenomena, such as shock-waves formation, can arise even if initial perturbations are confined in layers of linear dimensions very small compared to the dimensions of the medium. The occurring of critical times in a model of spherically symmetric self-gravitating interstellar gas cloud, suggests a mechanism in which the strong shock waves so generated might explain the formation of a cluster of protostars in the framework of the modern theory of Star Formation. A procedure is also described which let to overcome the solving of the wave front equation which turns out to be very useful in numerical applications.
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