带偏振的辐射传输方程的唯一可解性
On the unique solvability of radiative transfer equations with polarization
摘要：
研究了具有偏振和变折射率的辐射传输方程的适定性。适定性分析包括有界空间域上的非齐次边值问题，这需要分析合适的迹空间。此外，我们还讨论了矩阵值解的正性、厄米性和保范性。作为辅助结果，我们得到了矩阵乘积的新的迹不等式。
英文摘要：
We investigate the well-posedness of the radiative transfer equation with polarization and varying refractive index. The well-posedness analysis includes non-homogeneous boundary value problems on bounded spatial domains, which requires the analysis of suitable trace spaces. Additionally, we discuss positivity, Hermiticity, and norm-preservation of the matrix-valued solution. As auxiliary results, we derive new trace inequalities for products of matrices.
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