Positivity in Time Dependent Linear Transport Theory

Jürgen Voigt
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Jürgen Voigt: Universität Trier, Fach Mathematik

A chapter in Positive Semigroups of Operators, and Applications, 1984, pp 311-331 from Springer

Abstract: Abstract We present methods using positive semigroups and perturbation theory in the application to the linear Boltzmann equation. Besides being a review, this paper also presents generalizations of known results and develops known methods in a more abstract setting. In Section 1 we present spectral properties of the semigroup operators W a (t) of the absorption semigroup and its generator T a . In Section 2 we treat the full semigroup (W(t); t ≥ 0) as a perturbation of the absorption semigroup. We discuss part of the problems (perturbation arguments and existence of eigenvalues) which have to be solved in order to obtain statements about the large time behaviour ofW(·). In Section 3 we discuss irreducibility of W(·). In four appendices we present abstract methods used in Sections 1, 2 and 3.

Keywords: linear transport theory; neutron transport equation; Boltzmann equation; semigroups; perturbations; irreducibility; collision; absorption; scattering; spectrum; Dyson-Phillips expansion; flows (search for similar items in EconPapers)
Date: 1984
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DOI: 10.1007/978-94-009-6484-6_4

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