Year: 2024
Type: article
Abstract: In this paper, we derive sufficient conditions that guarantee an description of long-time asymptotic behavior of the solution to the Cauchy problem governed by a linear neutron transport equation with a partially elastic collision operator under periodic boundary conditions. Our strategy involves showing that the strongly continuous semigroups et(T+Ke)t≥0 and et(T+Kc+Ke)t≥0, generated by the operators T+Ke and T+Kc+Ke, respectively, have the same essential type. According to Proposition 1, it is sufficient to show that remainder term in the Dyson–Philips expansion is compact. Our analysis focuses on the compactness properties of the second-order remainder term in the Dyson–Phillips expansion related to the problem. We first show that R2(t) is compact on L2(Ω×V,dxdv), and, using an interpolation argument (see Proposition 2), we establish the compactness of R2(t) on Lp(Ω×V,dxdv)-spaces for 1
Source: Mathematics
DOI: 10.3390/math12223455
Authors: Abdul-Majeed Al-Izeri, Khalid Latrach
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $2,955
OpenAlex ID: W4404065053