Translator Disclaimer
Winter 2019 The structure of fractional spaces generated by a two-dimensional neutron transport operator and its applications
Allaberen Ashyralyev, Abdulgafur Taskin
Adv. Oper. Theory 4(1): 140-155 (Winter 2019). DOI: 10.15352/aot.1711-1261

Abstract

In this study, the structure of fractional spaces generated by the two-dimensional neutron transport operator $A$ defined by formula $Au=\omega_{1}\frac{\partial u}{\partial x}+\omega _{2}\frac{\partial u}{\partial y}$ is investigated. The positivity of $A$ in $C\left( \mathbb{R}^{2}\right)$ and $L_{p}\left( \mathbb{R}^{2}\right)$, $1\leq p \lt \infty$, is established. It is established that, for any $0 \lt \alpha \lt 1$ and $1\leq p \lt \infty$, the norms of spaces $E_{\alpha ,p}\left( L_{p}\left( \mathbb{R}^{2}\right), A\right)$ and $E_{\alpha }\left( C\left( \mathbb{R}^{2}\right), A\right) , W_{p}^{\alpha } \left( \mathbb{R}^{2}\right)$ and $C^{\alpha }\left( \mathbb{R}^{2}\right)$ are equivalent, respectively. The positivity of the neutron transport operator in Hölder space $C^{\alpha }\left( \mathbb{R}^{2}\right)$ and Slobodeckij space $W_{p}^{\alpha }\left( \mathbb{R}^{2}\right)$ is proved. In applications, theorems on the stability of Cauchy problem for the neutron transport equation in Hölder and Slobodeckij spaces are provided.

Citation

Download Citation

Allaberen Ashyralyev. Abdulgafur Taskin. "The structure of fractional spaces generated by a two-dimensional neutron transport operator and its applications." Adv. Oper. Theory 4 (1) 140 - 155, Winter 2019. https://doi.org/10.15352/aot.1711-1261

Information

Received: 12 November 2017; Accepted: 18 April 2018; Published: Winter 2019
First available in Project Euclid: 10 May 2018

zbMATH: 06946447
MathSciNet: MR3867338
Digital Object Identifier: 10.15352/aot.1711-1261

Subjects:
Primary: 47B65
Secondary: 34B27, 35A35, 35K30

Rights: Copyright © 2019 Tusi Mathematical Research Group

JOURNAL ARTICLE
16 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.4 • No. 1 • Winter 2019
Back to Top