Spectra of perturbed semigroups with applications to transport theory
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This article is published in Journal of Mathematical Analysis and Applications.The article was published on 1970-05-01 and is currently open access. It has received 156 citations till now. The article focuses on the topics: Linear transport theory & Neutron transport.read more
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Solution of a nonlinear Boltzmann equation for neutron transport in L1 space
TL;DR: In this paper, the authors give a constructive method for the solution of the Boltzmann equation for neutron transport in a bounded space domain subject to typical boundary and initial conditions, and sufficient conditions are given to insure the existence of a unique solution.
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Nonhomogeneous boundary conditions in neutron transport.
Janusz Mika,R. Stankiewicz +1 more
TL;DR: In this paper, a rigorous mathematical theory of the time-dependent neutron-transport equation with nonhomogeneous boundary conditions is developed, and the existence and uniqueness of the solution in the spaces of summable functions are demonstrated.
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Description of the real point spectrum for a class of neutron transport operators
TL;DR: In this article, the fine structure of the real point spectrum of a class of transport operators with unsymmetric scattering kernels was studied and necessary and sufficient conditions for existence, finiteness, and sufficient condition for infiniteness were given.
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A compactness result for perturbed semigroups and application to a transport model
TL;DR: In this article, the compactness properties of the remainder term of the Dyson-Phillips expansion of perturbed semigroups on general Banach spaces were studied. But the compactity properties of this term were not considered.
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Hypocoercivity with Schur complements
TL;DR: In this article , an approach to obtaining explicit estimates on the resolvent of hypocoercive operators by using Schur complements, rather than from an exponential decay of the evolution semigroup combined with a time integral, was proposed.
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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.
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On the spectrum of an unsymmetric operator arising in the transport theory of neutrons
Joseph Lehner,G. Milton Wing +1 more
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Existence and uniqueness of nonnegative eigenfunctions of the Boltzmann operator
TL;DR: In this article, the authors considered the initial value problem and showed that the decay constant X is an eigenvalue of the Boltzmann operator A. The exact domain of definition of A is dependent on the space of functions where A acts, and will be described in Section 2.