Homogenization of the linear Boltzmann equation with a highly oscillating scattering term in extended phase space

In this article, we rigorously prove the homogenization limit of the linear Boltz-mann equation when the scattering term is highly oscillating with respect to the velocity variable. We prove that the limit equation keeps, in a suitably extended phase space, the same structure as the non-homogenized one. This situation does not coincide with what happens in standard phase space, where the appearance of memory terms is expected. (c) 2023 Elsevier Ltd. All rights reserved.