L1 contraction property for a Boltzmann equation with Pauli statistics
Antoine Mellet, Benoı̂t Perthame · Comptes Rendus Mathématique · 2002
We establish a L 1 contraction property for solutions to the Boltzmann equation when collisions are taken into account through the Pauli operator. The Pauli operator is a non-linear integral operator, that we consider here in full generality, without assuming relations such as the detailed balance principle. It takes into account the Pauli exclusion principle and appears especially to describe the flow of electrons and holes in some semi-conductor devices.