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

Roman Romanov

doi:10.3934/krm.2012.5.113

Article Contents

2012, Volume 5, Issue 1: 113-128. Doi: 10.3934/krm.2012.5.113

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

Roman Romanov^1,

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

Received: July 31, 2010

Revised: July 31, 2011

Published: February 2012

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Abstract

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.

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Mathematics Subject Classification: Primary: 47A45; Secondary: 35Q20.

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References

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