A note on Fisher Information hypocoercive decay for the linear Boltzmann equation

Pierre Monmarché (1, 2)

1 LJLL - Laboratoire Jacques-Louis Lions
2 LCT - Laboratoire de chimie théorique

This note deals with the linear Boltzmann equation in the non-compact setting with a confining potential which is close to quadratic. We prove that in this case, starting from a smooth initial datum, the Fisher Information (hence, the relative entropy) with respect to the stationary state converges exponentially fast to zero.

Domaines: Probabilités [math.PR]; Equations aux dérivées partielles [math.AP]

Pierre Monmarché. A note on Fisher Information hypocoercive decay for the linear Boltzmann equation. 2018. ⟨hal-01716339⟩