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Hypocoercivity of linear kinetic equations via Harris's Theorem
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A. Cañizo, José, Cao, Chuqi, Evans, Josephine and Yoldaş, Havva (2020) Hypocoercivity of linear kinetic equations via Harris's Theorem. Kinetic & Related Models, 13 (1). pp. 97-128. doi:10.3934/krm.2020004
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Official URL: http://dx.doi.org/10.3934/krm.2020004
Abstract
We study convergence to equilibrium of the linear relaxation Boltzmann (also known as linear BGK) and the linear Boltzmann equations either on the torus (x,v)∈Td×Rd or on the whole space
(x,v)∈Rd×Rd with a confining potential. We present explicit convergence results in total variation or weighted total variation norms (alternatively L1 or weightedL1 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.
| Item Type: | Journal Article | |||||||||||||||||||||||||||
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| Subjects: | Q Science > QA Mathematics Q Science > QC Physics |
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| Divisions: | Faculty of Science > Mathematics | |||||||||||||||||||||||||||
| Library of Congress Subject Headings (LCSH): | Differential equations, Partial -- Asymptotic theory, Transport theory, Mathematical physics, Kinetic theory of matter, Evolution equations -- Numerical solutions | |||||||||||||||||||||||||||
| Journal or Publication Title: | Kinetic & Related Models | |||||||||||||||||||||||||||
| Publisher: | American Institute of Mathematical Sciences | |||||||||||||||||||||||||||
| ISSN: | 1937-5077 | |||||||||||||||||||||||||||
| Official Date: | 31 February 2020 | |||||||||||||||||||||||||||
| Dates: |
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| Volume: | 13 | |||||||||||||||||||||||||||
| Number: | 1 | |||||||||||||||||||||||||||
| Page Range: | pp. 97-128 | |||||||||||||||||||||||||||
| DOI: | 10.3934/krm.2020004 | |||||||||||||||||||||||||||
| Status: | Peer Reviewed | |||||||||||||||||||||||||||
| Publication Status: | Published | |||||||||||||||||||||||||||
| Publisher Statement: | The following article appeared in A. Cañizo, José, Cao, Chuqi, Evans, Josephine and Yoldaş, Havva (2020) Hypocoercivity of linear kinetic equations via Harris's Theorem. Kinetic & Related Models, 13 (1). pp. 97-128. and may be found at http://dx.doi.org/10.3934/krm.2020004 | |||||||||||||||||||||||||||
| Access rights to Published version: | Restricted or Subscription Access | |||||||||||||||||||||||||||
| RIOXX Funder/Project Grant: |
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