Estimates of solutions of linear neutron transport equation at large time and spectral singularities
Roman Romanov
Kinetic & Related Models 2012, 5(1): 113-128 doi: 10.3934/krm.2012.5.113
The spectral analysis of a dissipative linear transport operator with a polynomial collision integral by the Szőkefalvi-Nagy - Foiaş functional model is given. An exact estimate for the remainder in the asymptotic of the corresponding evolution semigroup is proved in the isotropic case. In the general case, it is shown that the operator has at most finitely many eigenvalues and spectral singularities and an absolutely continuous essential spectrum. An upper estimate for the remainder is established.
keywords: Transport equation spectral singularities asymptotics of semigroups.

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