# American Institute of Mathematical Sciences

March  2012, 5(1): 113-128. doi: 10.3934/krm.2012.5.113

## Estimates of solutions of linear neutron transport equation at large time and spectral singularities

 1 Laboratory of Quantum Networks and Department of Mathematical Physic, Faculty of Physics, St.Petersburg State University, 198504, Saint Petersburg, Russian Federation

Received  August 2010 Revised  August 2011 Published  January 2012

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.
Citation: Roman Romanov. Estimates of solutions of linear neutron transport equation at large time and spectral singularities. Kinetic & Related Models, 2012, 5 (1) : 113-128. doi: 10.3934/krm.2012.5.113
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