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Geometry and Topology Seminar: Lili Yan, University of Minnesota, Stable determination of time-dependent collision kernel in the nonlinear Boltzmann equation
November 10, 2023 | 1:10 pm - 2:00 pm EST
In this talk, we consider an inverse problem for the nonlinear Boltzmann equation with a time-dependent kernel in dimensions 2 and higher. 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. This is based on joint work with Ru-Yu Lai.