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Existence of Invariant Densities and Time Asymptotics of Conservative Linear Kinetic Equations on the Torus Without Spectral Gaps

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Abstract

This work deals with general linear conservative neutron transport semigroups without spectral gaps in \(L^{1}(\mathcal{T}^{n}\times \mathbb{R} ^{n})\) where \(\mathcal{T}^{n}\) is the \(n\)-dimensional torus. We study the mean ergodicity of such semigroups and their strong convergence to their ergodic projections as time goes to infinity. Systematic functional analytic results are given.

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

    Mustapha Mokhtar-Kharroubi

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  1. Mustapha Mokhtar-Kharroubi
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Correspondence to Mustapha Mokhtar-Kharroubi.

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Mokhtar-Kharroubi, M. Existence of Invariant Densities and Time Asymptotics of Conservative Linear Kinetic Equations on the Torus Without Spectral Gaps. Acta Appl Math 175, 8 (2021). https://doi.org/10.1007/s10440-021-00435-0

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