Problems on gravitational collapse of interstellar gas clouds. II

The gravitational collapse of a spherically symmetric interstellar gas cloud has been investigated following the non-linear discontinuity waves propagation theory. It has been pointed out that macroscopic phenomena, such as the process of fragmentation, can arise (shock wave formation) - even in the case of spherical symmetry - at times smaller than the free-fall time tsub(ff), provided the initial data of the Cauchy problem be discontinuous within a sphere of radius R(mean) < Rsub(cloud) (caustic cases). It has also been proved that strong discontinuities outside the mentioned sphere may generate critical times tsub(cr) < tsub(ff) (depending on the typical non-linear structure of the differential system). The cooling-heating function plays an important role in contrasting the formation of shock waves. (Auth.)