POSITIVITY OF THE DIFFERENCE
NEUTRON TRANSPORT OPERATOR
Allaberen Ashyralyev1,2,3, Abdulgafur Taskin4
1Department of Mathematics, Near East University
Nicosia, TRNC, Mersin 10, TURKEY
2Peoples’ Frienship University of Russia (RUDN University)
Ul Mikluko Maklaya 6, Moscow 117198, RUSSIAN Federation
3Institute of Mathematics and Mathematical Modeling
Almaty, 050010, KAZAKHSTAN
4ENKA Schools, Istinye, Istanbul - 34460, TURKEY

Abstract

In the present study, a two-dimensional difference neutron transport operator is considered. The resolvent equation for this neutron transport operator is constructed. The positivity of this difference neutron transport operator L1(R(r,h)2) is provided. The structure of fractional spaces generated by the two-dimensional difference neutron transport operator is studied. It is established that the norms in the spaces Eα,1(L1(R(r,h)2),Ar,h) and Wα1(R(r,h)2) are equivalent. This result enabled us to prove the positivity of the difference neutron transport operator in the Slobodeckij space. In practice, the theorem on the stability of the Cauchy problem for the difference neutron transport equation in Banach spaces is presented.

Citation details of the article



Journal: International Journal of Applied Mathematics
Journal ISSN (Print): ISSN 1311-1728
Journal ISSN (Electronic): ISSN 1314-8060
Volume: 34
Issue: 2
Year: 2021

DOI: 10.12732/ijam.v34i2.9

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