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.

中文翻译：

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无谱隙环面上保守线性动力学方程的不变密度和时间渐近的存在性

这项工作处理在\(L^{1}(\mathcal{T}^{n}\times \mathbb{R} ^{n})\)中没有光谱间隙的一般线性保守中子输运半群，其中\(\mathcal {T}^{n}\)是\(n\)维环面。我们研究了这种半群的平均遍历性以及它们随着时间趋于无穷大而强烈收敛于它们的遍历预测。给出了系统的泛函分析结果。