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Positivity in Time Dependent Linear Transport Theory

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Positive Semigroups of Operators, and Applications

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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.

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Author information

Authors and Affiliations

  1. Fach Mathematik, Universität Trier, F.R Germany

    Jürgen Voigt

  2. Mathematisches Institut der Universität München, Theresienstraße 39, D-8000, München 2, Federal Republic of Germany

    Jürgen Voigt

Authors
  1. Jürgen Voigt
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Editor information

Editors and Affiliations

  1. Mathematics Institute, University of Trondheim, Norway

    Ola Bratteli

  2. Dept. of Mathematics/E1, University of Pennsylvania, Philadelphia, USA

    Palle E. T. Jørgensen

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© 1984 D. Reidel Publishing Company

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Voigt, J. (1984). Positivity in Time Dependent Linear Transport Theory. In: Bratteli, O., Jørgensen, P.E.T. (eds) Positive Semigroups of Operators, and Applications. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-6484-6_4

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  • DOI: https://doi.org/10.1007/978-94-009-6484-6_4

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-009-6486-0

  • Online ISBN: 978-94-009-6484-6

  • eBook Packages: Springer Book Archive

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