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arXiv · 2011.11582

Damping of kinetic transport equation with diffuse boundary condition

Jiaxin Jin·Chanwoo Kim
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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 $\mathbb{R}^3$ with the smooth boundary of the diffuse boundary condition. We prove the theorem by establishing a novel $L^1$-$L^\infty$ framework via stochastic cycles.

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Jiaxin Jin, Chanwoo Kim. 2020-11-23. Damping of kinetic transport equation with diffuse boundary condition. https://arxiv.org/abs/2011.11582

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