An Lp theory for stationary radiative transfer
An Lp theory for stationary radiative transfer
复制标题
静态辐射传输的 Lp 理论
DOI：
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发表时间：
2013
期刊：
影响因子：
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通讯作者：
M. Schlottbom
中科院分区：
文献类型：
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作者：
H. Egger;M. Schlottbom
摘要本文对加权空间中的定态辐射传输方程进行了完备的分析。加权空间的使用使我们能够在最小的参数假设下得到一致的先验估计。通过构造一个显式的例子，我们表明我们的估计是尖锐的，一般不能提高。然而，更好的估计是根据对参数的额外假设得出的。我们还提出了解的导数和迹的估计，并制定了一个自然的能量空间，其中数据到解的映射成为同构。作为一个副产品，我们能够证明一致收敛的源迭代的所有没有假设的正吸收，经常在文献中使用。
Abstract We present a self-contained analysis of the stationary radiative transfer equation in weighted spaces. The use of weighted spaces allows us to derive uniform a-priori estimates for under minimal assumptions on the parameters. By constructing an explicit example, we show that our estimates are sharp and cannot be improved in general. Better estimates are, however, derived under additional assumptions on the parameters. We also present estimates for derivatives and traces of the solution and formulate a natural energy space, for which the data-to-solution map becomes an isomorphism. As a side result, we are able to prove uniform convergence of the source iteration for all without the assumption of positive absorption that is frequently used in the literature.