Hypocoercivity and exponential time decay for the linear inhomogeneous relaxation Boltzmann equation

Article type: Research Article

Authors: Hérau, Frédéric

Affiliations: Laboratoire de Mathématiques, UFR Sciences exactes et naturelles, Université de Reims Champagne-Ardenne, Moulin de la Housse, BP 1039 51687 Reims cedex 9 E-mail: herau@univ-reims.fr

Abstract: We consider an inhomogeneous linear Boltzmann equation, with an external confining potential. The collision operator is a simple relaxation toward a local Maxwellian, therefore without diffusion. We prove the exponential time decay toward the global Maxwellian, with an explicit rate of decay. The methods are based on hypoelliptic methods transposed here to get spectral information. They were inspired by former works on the Fokker–Planck equation and the main feature of this work is that they are relevant although the equation itself has no regularizing properties.

Journal: Asymptotic Analysis, vol. 46, no. 3-4, pp. 349-359, 2006