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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One-Parameter Semigroups for Linear Evolution Equations
Klaus-Jochen Engel,Rainer Nagel +1 more
TL;DR: In this paper, Spectral Theory for Semigroups and Generators is used to describe the exponential function of a semigroup and its relation to generators and resolvents.
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Diffusion approximation and computation of the critical size
TL;DR: In this article, the authors studied the spectral properties of the transport equation and how the diffusion approximation is related to the computation of the critical size, and they showed that when the transport operator is almost conservative, the critical value of the parameter 17 is large and it is exactly for this range of value that the diffusion approximation is accurate.
Book
Boundary Value Problems in Abstract Kinetic Theory
TL;DR: In this paper, the authors present a survey of abstract kinetic theory and its application in various areas of physics, chemistry, biology, and engineering, including radiative transfer and rarefied gas dynamics.
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Invariant Manifolds for Semilinear Partial Differential Equations
TL;DR: The stable, unstable and centre manifolds as discussed by the authors are invariant under the flow relative to a neighbourhood of the equilibrium point and carry the solutions that decay or grow (or neither) at certain rates.
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A partial differential equation with infinitely many periodic orbits: Chaotic oscillations of a forced beam
Philip Holmes,Jerrold E. Marsden +1 more
TL;DR: In this article, a class of time-periodically perturved evolution equations in a space whose associated Poincar´e map contains a Smale horseshoe is delineated.
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Journal ArticleDOI
Complete continuity of the free gas scattering operator in neutron thermalization theory
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Effective solution to the initial value problem in neutron thermalization theory
TL;DR: In this article, an effective solution to the initial value problem in neutron thermalization assuming isotropic scattering of neutrons is given for two typical geometries: an infinite slab and a bounded convex body.