ON THE ASYMPTOTIC SPECTRUM OF A TRANSPORT OPERATOR WITH ELASTIC AND INELASTIC COLLISION OPERATORS

doi:10.1007/s10473-020-0315-2

Acta mathematica scientia,Series B ›› 2020, Vol. 40 ›› Issue (3): 805-823.doi: 10.1007/s10473-020-0315-2

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ON THE ASYMPTOTIC SPECTRUM OF A TRANSPORT OPERATOR WITH ELASTIC AND INELASTIC COLLISION OPERATORS

Abdul-Majeed AL-IZERI, Khalid LATRACH

Université Clermont Auvergne, CNRS, LMBP, F-63000 Clermont-Ferrand, France

Received:2018-09-27 Revised:2019-09-04 Online:2020-06-25 Published:2020-07-17
Contact: Khalid LATRACH E-mail:khalid.latrach@uca.fr

Abstract

Abstract: In this article, we investigate the spectral properties of a class of neutron transport operators involving elastic and inelastic collision operators introduced by Larsen and Zweifel[1]. Our analysis is manly focused on the description of the asymptotic spectrum which is very useful in the study of the properties of the solution to Cauchy problem governed by such operators (when it exists). The last section of this work is devoted to the properties of the leading eigenvalue (when it exists). So, we discuss the irreducibility of the semigroups generated by these operators. We close this section by discussing the strict monotonicity of the leading eigenvalue with respect to the parameters of the operator.

Key words: Compactness properties, transport operator, abstract boundary conditions, asymptotic spectrum, irreducibility, leading eigenvalue

CLC Number:

47A10

Abdul-Majeed AL-IZERI, Khalid LATRACH. ON THE ASYMPTOTIC SPECTRUM OF A TRANSPORT OPERATOR WITH ELASTIC AND INELASTIC COLLISION OPERATORS[J].Acta mathematica scientia,Series B, 2020, 40(3): 805-823.

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ON THE ASYMPTOTIC SPECTRUM OF A TRANSPORT OPERATOR WITH ELASTIC AND INELASTIC COLLISION OPERATORS

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