Diffusion Approximation of An Inelastic Scattering Model in Linear Kinetic Theory

摘要

In this paper we perform an asymptotic analysis of a singularly perturbed linear Boltzmann equation with inelastic scattering operator, when the parameter corresponding to the mean free path of particles tends to zero. A characteristic feature of this operator, which makes it different from standard linear Boltzmann operators, is that it has infinitely many invariants; it is also unbounded for small velocities. We find the diffusion equation approximating collision invariants, determine conditions for existence of the initial layer and provide estimates of the error of approximation in the space L_1.