The existence of moments of solutions to transport equations with inelastic scattering and their application in the asymptotic analysis (Q2706911)

The author considers the time-dependent spatially homogeneous Boltzmann equation for combined elastic and inelastic isotropic scattering in the Lorentz gas limit (such model can describe various electron and neutron transport processes in gases in solids, in particular, in semiconductors). Using the theory of resolvent positive operators and Desch perturbation theorem, the author proves existence of all moments of solutions to the above equation (the key step in the proof is the fact that the corresponding integral operator generates a positive semigroup). Additionally, the author investigates Cauchy problem for the kinetic equation with dominant elastic scattering, obtains an asymptotic solution, and gives error estimates in the \(L_1\)-norm.