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arXiv · 2309.03368

Stable determination of time-dependent collision kernel in the nonlinear Boltzmann equation

Ru-Yu Lai·Lili Yan
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Abstract

We consider an inverse problem for the nonlinear Boltzmann equation with a time-dependent kernel in dimensions $n\ge 2$. We establish a logarithm-type stability result for the collision kernel from measurements under certain additional conditions. A uniqueness result is derived as an immediate consequence of the stability result. Our approach relies on second-order linearization, multivariate finite differences, as well as the stability of the light-ray transform.

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Ru-Yu Lai, Lili Yan. 2023-09-06. Stable determination of time-dependent collision kernel in the nonlinear Boltzmann equation. https://arxiv.org/abs/2309.03368

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