2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/121042For the spatially homogeneous Boltzmann equation with cutoff hard potentials it is shown that solutions remain bounded from above, uniformly in time, by a Maxwellian distribution, provided the initial data have a Maxwellian upper bound. The main technique is based on a comparison principle that uses a certain dissipative property of the linear Boltzmann equation. Implications of the technique to propagation of upper Maxwellian bounds in the spatially-inhomogeneous case are discussed.Analysis of PDEsMathematical Physics82C40, 35B05, 76P05text