On the unique solvability of radiative transfer equations with polarization

Vincent Bosboom; Matthias Schlottbom; Felix L. Schwenninger

doi:10.48550/arXiv.2203.03233

On the unique solvability of radiative transfer equations with polarization

Vincent Bosboom, Matthias Schlottbom^*, Felix L. Schwenninger

^*Corresponding author for this work

Research output: Working paper

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Abstract

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.

Original language	English
Publisher	ArXiv.org
DOIs	https://doi.org/10.48550/arXiv.2203.03233
Publication status	Submitted - 7 Mar 2022

Keywords

Radiative transfer
polarization
Well-posedness
Semigroup
Refractive index

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10.48550/arXiv.2203.03233

2203.03233Submitted version, 509 KB

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abstract = "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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AU - Schwenninger, Felix L.

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AB - 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.

KW - Radiative transfer

KW - polarization

KW - Well-posedness

KW - Semigroup

KW - Refractive index

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DO - 10.48550/arXiv.2203.03233

M3 - Working paper

BT - On the unique solvability of radiative transfer equations with polarization

PB - ArXiv.org

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On the unique solvability of radiative transfer equations with polarization

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Keywords

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