Estimates of solutions of linear neutron transport equation at large time and spectral singularities (Q450070)

Using the method of the Sz.-Nagy-Foias model, the spectral analysis of a dissipative linear transport operator is studied. A power upper estimate for the reminder in the case of a polynomial collision integral is established and a precise estimate in the isotropic case is obtained. The paper is organized in four sections. After an introduction and a presentation of the main results (Theorems A and B), in the second section absolutely continuous subspaces are analyzed and the Nagy-Foias criterion is presented. In the third and fourth sections, estimates of solutions of the linear neutron transport equation at large time and spectral singularities are analyzed in anysotropic, respectively in the isotropic case, proving the main Theorems A and B.