Sebastian Throm:
The 1d inelastic Boltzmann equation for moderately hard potentials
Time and place
Tuesday, 17.12.24, 14:15-15:15, Raum 226, Hermann-Herder-Str. 10
Abstract
Inelastic interaction of granular matter is a common phenomenon in natural processes. A mathematical description of such behaviour is given by a modification of the Boltzmann equation, where the dissipation of kinetic energy during collisions characterises the inelasticity at the particle level.\n\nIn this talk, we consider the occurrence of self-similar behaviour in the long-time limit for the one-dimensional inelastic Boltzmann equation. More precisely, we prove that self-similar profiles are unique in the regime of moderately hard potentials. The proof relies on a perturbation argument from the Maxwell model, together with a spectral gap for the corresponding linearised operator.