Analysis of the M1 model: Well-posedness and diffusion asymptotics
Analysis of the M1 model: Well-posedness and diffusion asymptotics
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DOI：
10.1016/j.jmaa.2013.01.042
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发表时间：
2013-06
影响因子：
1.3
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中科院分区：
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本文对辐射传输理论中的M1模型进行了分析。该模型的推导是基于熵最小化原理，这导致一个双曲系统的平衡律松弛。在多维情形下，我们在适当的小性条件下建立了全局光滑解的存在唯一性。在一维的情况下，我们表明，小的条件并不依赖于粒子的平均自由程，使我们也可以严格证明该模型的扩散渐近的一致性。结果扩展了Coulombel等人的分析。[J. F. Coulombel，F. Golse T. Goudon，Diffusion approximation and entropy-based moment closure for kinetic equations，Asymptotic Analysis，45（2005）1-39]到其中熵泛函解释朝向普朗克状态的弛豫的情况，这在物理上更相关。
This paper is devoted to the analysis of the M1 model which arises in radiative transfer theory. The derivation of the model is based on the entropy minimization principle, which leads to a hyperbolic system of balance laws with relaxation. In the multi-dimensional case, we establish the existence–uniqueness of a globally defined smooth solution under a suitable smallness condition on the initial data. In the one-dimensional case we show that the smallness condition does not depend on the particles mean free path so that we can also rigorously justify the consistency of the model with the diffusion asymptotics. The result extends the analysis of Coulombel et al. [J.-F. Coulombel, F. Golse T. Goudon, Diffusion approximation and entropy-based moment closure for kinetic equations, Asymptotic Analysis, 45 (2005) 1–39] to the case where the entropy functional accounts for relaxation towards the Planckian state, which is physically more relevant.