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arXiv · 2309.15758

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

Yuzhe Zhu
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Abstract

We establish $L^2$-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 $L^2$ is also derived under general Maxwell boundary conditions. The proofs are simply based on energy estimates together with previous ideas from $L^2$-hypocoercivity and relative entropy methods.

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Yuzhe Zhu. 2023-09-27. A note on asymptotics of linear dissipative kinetic equations in bounded domains. https://doi.org/10.2140/paa.2024.6.977

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