# Analyse spectrale de modèles neutroniques

Abstract : This dissertation is mainly devoted to spectral analysis of various neutron transport models. It is composed of three complementary parts. Part 1 deals with spectral mapping theorems in unbounded geometries where, due to the lack of compactness, the classical arguments do not work. Using some functional analytic results on the critical spectrum of perturbed semigroups, we show under fairly general assumptions that the spectral mapping theorem holds. In Part 2 we provide a new approach, called resolvent approach, to study the stability of essential and critical spectra of perturbed $C_(0)$-semigroups on Hilbert spaces. We show how these results apply to neutron transport equations in both bounded or unbounded geometries. The third part deals with a partly elastic collision model introduced by E.W. Larsen and P.F. Zweifel. To display the large time behavior of the semigroup governing this model, we present its spectral theory. We analyze compactness properties related to the model, which enable us, in particular, to derive some stability results on the essential type. Then we examine the incidences of the positivity: irreducibility, strict monotonicity properties of the leading eigenvalue, reality of the peripheral spectrum.
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Cited literature [114 references]

https://tel.archives-ouvertes.fr/tel-00011072
Contributor : Mohammed Sbihi <>
Submitted on : Monday, November 21, 2005 - 6:54:16 PM
Last modification on : Thursday, January 28, 2021 - 10:26:02 AM
Long-term archiving on: : Friday, September 14, 2012 - 3:40:29 PM

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• HAL Id : tel-00011072, version 1

### Citation

Mohammed Sbihi. Analyse spectrale de modèles neutroniques. Mathématiques [math]. Université de Franche-Comté, 2005. Français. ⟨tel-00011072⟩

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