Supports of measure solutions for spatially homogeneous Boltzmann equations (Q857624)

The authors consider the spatially homogeneous Boltzmann type equation (in the velocity vector space \(\mathbb{R}^3\)) and obtain a lower bound for the solution. The initial distribution considered can be a measure. The result obtained implies that, if the initial distribution is not a Dirac measure, then for any \(t> 0\) and for any open set of the velocity vector space \(\mathbb{R}^3\) the measure of the solution is strictly positive, that is, the solution is supported by the whole \(\mathbb{R}^3\).