Hypocoercivity of linear kinetic equations via harris's theorem

José A. Cañizo, Chuqi Cao*, Josephine Evans, Havva Yoldaş

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

7 Citations (Scopus)


We study convergence to equilibrium of the linear relaxation Boltz-mann (also known as linear BGK) and the linear Boltzmann equations either on the torus (x, v) ε Td x Rd or on the whole space (x, v) ε Rd x Rd with a confining potential. We present explicit convergence results in total variation or weighted total variation norms (alternatively L1 or weighted L1 norms). The convergence rates are exponential when the equations are posed on the torus, or with a confining potential growing at least quadratically at infinity. Moreover, we give algebraic convergence rates when subquadratic potentials considered. We use a method from the theory of Markov processes known as Harris's Theorem.

Original languageEnglish
Pages (from-to)97-128
Number of pages32
JournalKinetic and Related Models
Issue number1
Publication statusPublished - 2020
Externally publishedYes


  • Harris's theorem
  • Hypocoercivity
  • Kinetic theory
  • Linear boltzmann equation
  • Linear relaxation boltzmann equation


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