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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Unstable oscillatory-tail waves in collisionles plasmas
Yan Guo,Walter A. Strauss +1 more
TL;DR: In this paper, it was shown that a collisionless relativistic neutral plasma is nonlinearly dynamically unstable under certain perturbations of the initial data and that such a state is not stable.
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Large-time decay of the soft potential relativisticBoltzmann equation in $\mathbb{R}^3_x$
Robert M. Strain,Keya Zhu +1 more
TL;DR: For the relativistic Boltzmann equation, the authors proves the global existence, uniqueness, positivity, and optimal time convergence rate for solutions which start out sufficiently close under the general physical soft potential assumption.
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Geometric Analysis of the Linear Boltzmann Equation I. Trend to Equilibrium
TL;DR: In this paper, the authors study how the association of transport and collision phenomena can lead to convergence to equilibrium, using concepts and ideas from control theory, and show that convergence towards an equilibrium is equivalent to an almost everywhere geometric control condition.
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Phase Transition in a Vlasov-Boltzmann Binary Mixture
TL;DR: In this article, a binary mixture over a line with collisions and long range repulsive interaction between different species is considered, and it undergoes a segregation phase transition at sufficiently low temperature.
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Magnetically created instability in a collisionless plasma
Yan Guo,Walter A. Strauss +1 more
TL;DR: In this paper, it was shown that there are homogeneous equilibria that are monotone decreasing in every direction and are arbitrarily close to a Vlasov-Maxwellian.
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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.