Stable Determination of Time-Dependent Collision Kernel in the Nonlinear Boltzmann Equation

Source abstract

Abstract. We consider an inverse problem for the nonlinear Boltzmann equation with a time-dependent kernel in dimensions [Formula: see text]. 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 and multivariate finite differences, as well as the stability of the light-ray transform.