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 trr, provided the initial data of tile Cauchy problem be discontinuous within a sphere of radius < Rc~oud (caustic cases). It has also been proved that strong discontinuities outside the mentioned sphere may generate critical times tot < trr (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.
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