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We consider an inverse problem for the nonlinear Boltzmann equation with atime-dependent kernel in dimensions $n\ge 2$. We establish a logarithm-typestability result for the collision kernel from measurements under certainadditional conditions. A uniqueness result is derived as an immediateconsequence of the stability result. Our approach relies on second-orderlinearization, multivariate finite differences, as well as the stability of thelight-ray transform.

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