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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

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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
Subjects: Q Science > QA Mathematics
Q Science > QC Physics
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:
DateEvent
31 February 2020Published
9 December 2020Available
1 July 2019Accepted
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:
Project/Grant IDRIOXX Funder NameFunder ID
MTM2014-52056-PMinisterio de Economía, Industria y Competitividad, Gobierno de EspañaUNSPECIFIED
MTM2017-85067-PMinisterio de Economía, Industria y Competitividad, Gobierno de EspañaUNSPECIFIED
UNSPECIFIED[ERDF] European Regional Development Fundhttp://dx.doi.org/10.13039/501100008530
UNSPECIFIEDInstitut d'aménagement et d'urbanisme de la région d'Île-de-FranceUNSPECIFIED
UNSPECIFIEDMinisterio de Economía, Industria y Competitividad, Gobierno de EspañaUNSPECIFIED
EP/L016516/1[EPSRC] Engineering and Physical Sciences Research Councilhttp://dx.doi.org/10.13039/501100000266
MAFRANEuropean Research Councilhttp://dx.doi.org/10.13039/501100000781
ANR-17-CE40-0030Universität Bielefeld. Forschungsschwerpunkt Mathematisierunghttp://viaf.org/viaf/130394048

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