Damping of kinetic transport equation with diffuse boundary condition

2020/11/23 by Jiaxin Jin, Chanwoo Kim, Jin, Jiaxin +1
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Probability (math.PR) #math.AP #math.PR

paper · pdf · doi:10.48550/arxiv.2011.11582

15 pages

arxiv created 2021/03/26 · arxiv updated 2021/03/29

Abstract

We prove that exponential moments of a fluctuation of the pure transport equation decay pointwisely almost as fast as t^-3 when the domain is any general strictly convex subset of ℝ³ with the smooth boundary of the diffuse boundary condition. We prove the theorem by establishing a novel L¹-L^∞ framework via stochastic cycles.

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