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A note on asymptotics of linear dissipative kinetic equations in bounded domains

Yuzhe Zhu
Vol. 6 (2024), No. 4, 977–994
DOI: 10.2140/paa.2024.6.977
Abstract

We establish L2-exponential decay properties for linear dissipative kinetic equations, including the time-relaxation and Fokker–Planck models, in bounded spatial domains with general boundary conditions that may not conserve mass. Their diffusion asymptotics in L2 is also derived under general Maxwell boundary conditions. The proofs are simply based on energy estimates together with previous ideas from L2-hypocoercivity and relative entropy methods.

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Keywords
dissipative kinetic equation, diffusion asymptotics, hypocoercivity, boundary condition
Mathematical Subject Classification
Primary: 35B40, 35Q62, 82C31, 82C40, 82C70
Milestones
Received: 23 August 2023
Revised: 12 August 2024
Accepted: 9 October 2024
Published: 17 November 2024
Authors
Yuzhe Zhu
Department of Pure Mathematics and Mathematical Statistics
University of Cambridge
Cambridge
United Kingdom		 Department of Mathematics
University of Chicago
Chicago, IL
United States
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