On the rate of convergence to equilibrium for the linear Boltzmann equation with soft potentials

Cañizo, José A.; Einav, Amit; Lods, Bertrand

Abstract

In this work we present several quantitative results of convergence to equilibrium for the linear Boltzmann operator with soft potentials under Grad's angular cut-off assumption. This is done by an adaptation of the famous entropy method and its variants, resulting in explicit algebraic, or even stretched exponential, rates of convergence to equilibrium under appropriate assumptions. The novelty in our approach is that it involves functional inequalities relating the entropy to its production rate, which have independent applications to equations with mixed linear and non-linear terms. We also briefly discuss some properties of the equation in the non-cut-off case and conjecture what we believe to be the right rate of convergence in that case.

Citation

Cañizo, J. A., Einav, A., & Lods, B. (2018). On the rate of convergence to equilibrium for the linear Boltzmann equation with soft potentials. Journal of Mathematical Analysis and Applications, 462(1), 801-839. https://doi.org/10.1016/j.jmaa.2017.12.052

• Journal Article Type: Article
• Acceptance Date: Nov 20, 2017
• Online Publication Date: Dec 20, 2017
• Publication Date: May 30, 2018
• Deposit Date: Nov 16, 2020
• Journal: Journal of Mathematical Analysis and Applications
• Print ISSN: 0022-247X
• Electronic ISSN: 1096-0813
• Publisher: Elsevier
• Peer Reviewed: Peer Reviewed
• Volume: 462
• Issue: 1
• Pages: 801-839
• DOI: https://doi.org/10.1016/j.jmaa.2017.12.052
• Public URL: https://durham-repository.worktribe.com/output/1285771