Asymptotic spectrum of the linear Boltzmann equation with general boundary conditions in finite bodies

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:448

Article

Kosad, Youssouf¹  Latrach, Khalid¹ 

[1] Univ Blaise Pascal Clermont II, Lab Math, CNRS, UMR 6620, Campus Univ Cezeaux,3 Pl Vasarely, F-63178 Aubiere, France

关键词: Transport operator;    General boundary conditions;    Asymptotic spectrum;    Positivity in the lattice sense;    Irreducibility;    Leading eigenvalue;   

DOI  :  10.1016/j.jmaa.2016.10.067

来源: Elsevier

【 摘 要 】

The purpose of this paper is the study of the spectral properties of both streaming operator and transport operator with general boundary conditions in multidimensional bounded geometry. We discuss the asymptotic spectrum: existence and nonexistence results of eigenvalues in the half-plane {gimel is an element of C : Re gimel > s(T-H)} where s(T-H) stands for the spectral bound of the streaming operator TH. Next, we discuss the irreducibility of the transport semigroup. In particular, we establish that the transport semigroup is irreducible if the boundary operator is strictly positive. Afterwards, we discuss the strict monotonicity of the leading eigenvalue (when it exists) of the transport operator with respect to different parameters of the equation. Our analysis is based essentially on results from the theory of positive linear operators. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

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