Journal ArticleDOI
Neutron Transport in a Nonuniform Slab with Generalized Boundary Conditions
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In this paper, the authors prove the existence and uniqueness of the solution of the initial value problem for neutron transport in a nonuniform slab with generalized boundary conditions, which include the vacuum and the perfect reflection boundary conditions as particular cases.Abstract:
We prove the existence and the uniqueness of the solution of the initial‐value problem for neutron transport in a nonuniform slab with generalized boundary conditions, which include the vacuum and the perfect reflection boundary conditions as particular cases Moreover, we show that the position‐dependent transport operator has at least one real eigenvalue and we indicate the asymptotic behavior of the neutron density as t → + ∞read more
Citations
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Journal ArticleDOI
Compactness properties for linear transport operators with abstract boundary conditions in slab geometry
TL;DR: In this article, the authors give necessary and sufficient conditions for some power of (λ-T)-1 K to be compact where T is the streaming operator and K the scattering operator.
Journal ArticleDOI
On the essential spectrum of transport operators on L1‐spaces
Khalid Latrach,Aref Jeribi +1 more
TL;DR: In this paper, the stability of the essential spectrum of a one-dimensional transport operator with general boundary conditions where an abstract boundary operator relates the incoming and the outgoing fluxes is established.
Journal ArticleDOI
Some remarks on the essential spectrum of transport operators with abstract boundary conditions
TL;DR: In this paper, the essential spectrum of the one-dimensional transport operator with general boundary conditions where an abstract boundary operator relates the incoming and the outgoing fluxes has been analyzed, and sufficient conditions are given in terms of boundary and collision operators assuring the stability of the spectrum.
Journal ArticleDOI
Fredholm Operators and Riesz Theory for Polynomially Compact Operators
Aref Jeribi,Nedra Moalla +1 more
TL;DR: In this article, a characterization of bounded Fredholm operators on a Banach space is given, which is used to describe the Riesz-Schauder theory of compact operators in the more general setting of polynomially compact operators.
Journal ArticleDOI
On General Transport Equations with Abstract Boundary Conditions. The Case of Divergence Free Force Field
TL;DR: In this article, the authors investigate well-posedness of transport equations with general external fields and general measures associated to boundary conditions modeled by abstract boundary operators H. Cessenat.
References
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Book
Perturbation theory for linear operators
TL;DR: The monograph by T Kato as discussed by the authors is an excellent reference work in the theory of linear operators in Banach and Hilbert spaces and is a thoroughly worthwhile reference work both for graduate students in functional analysis as well as for researchers in perturbation, spectral, and scattering theory.
Journal ArticleDOI
Lecons d'Analyse Fonctionelle.
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