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Spectral Theory for Neutron Transport

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Evolutionary Equations with Applications in Natural Sciences

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 2126))

Abstract

These notes resume a lecture given in the Cimpa School “Evolutionary equations with applications in natural sciences” held in South Africa (Muizenberg, July 22–August 2, 2013). However, the oral style of the lecture has been changed and the bibliography augmented. This version benefited also from helpful remarks and suggestions of a referee whom I would like to thank. The notes deal with various functional analytic tools and results around spectral analysis of neutron transport-like operators. A first section gives a detailed introduction (mostly without proofs) to fundamental concepts and results on spectral theory of (non-selfadjoint) operators in Banach spaces; in particular, we provide an introduction to spectral analysis of semigroups in Banach spaces and its consequences on their time asymptotic behaviour as time goes to infinity.

In memory of Seiji Ukaï

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  1. Département de Mathématiques, CNRS UMR 6623, Université de Franche-Comté, 16 Route de Gray, 25030, Besançon, France

    Mustapha Mokhtar-Kharroubi

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  1. Mustapha Mokhtar-Kharroubi
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  1. School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Durban, South Africa

    Jacek Banasiak

  2. Département de Mathématiques, UFR des Sciences et Techniques, Besançon, France

    Mustapha Mokhtar-Kharroubi

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Mokhtar-Kharroubi, M. (2015). Spectral Theory for Neutron Transport. In: Banasiak, J., Mokhtar-Kharroubi, M. (eds) Evolutionary Equations with Applications in Natural Sciences. Lecture Notes in Mathematics, vol 2126. Springer, Cham. https://doi.org/10.1007/978-3-319-11322-7_7

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