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arXiv · 2003.09549

Reconstruction of the collision kernel in the nonlinear Boltzmann equation

Ru-Yu Lai·Gunther Uhlmann·Yang Yang
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Abstract

We consider an inverse problem for the Boltzmann equation with nonlinear collision operator in dimensions $n\geq 2$. We show that the kinetic collision kernel can be uniquely determined from the incoming-to-outgoing mappings on the boundary of the domain provided that the kernel satisfies a monotonicity condition. Furthermore, a reconstruction formula is also derived. The key methodology is based on the higher-order linearization scheme to reduce a nonlinear equation into simpler linear equations by introducing multiple small parameters into the original equation.

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Ru-Yu Lai, Gunther Uhlmann, Yang Yang. 2020-03-21. Reconstruction of the collision kernel in the nonlinear Boltzmann equation. https://arxiv.org/abs/2003.09549

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