On the unique solvability of radiative transfer equations with polarization

Vincent Bosboom; Matthias Schlottbom; Felix L. Schwenninger

doi:10.1016/j.jde.2024.02.022

On the unique solvability of radiative transfer equations with polarization

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

^*Corresponding author for this work

Research output: Contribution to journal › Article › Academic › peer-review

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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
Pages (from-to)	174-203
Number of pages	30
Journal	Journal of differential equations
Volume	393
DOIs	https://doi.org/10.1016/j.jde.2024.02.022
Publication status	Published - 5 Jun 2024

Keywords

UT-Hybrid-D
Radiative transfer
Refractive index
Semigroup theory
Well-posedness
Polarization

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10.1016/j.jde.2024.02.022Licence: CC BY

1-s2.0-S0022039624000925-mainFinal published version, 425 KBLicence: CC BY

Cite this

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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.",

keywords = "UT-Hybrid-D, Radiative transfer, Refractive index, Semigroup theory, Well-posedness, Polarization",

author = "Vincent Bosboom and Matthias Schlottbom and Schwenninger, {Felix L.}",

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AU - Bosboom, Vincent

AU - Schlottbom, Matthias

AU - Schwenninger, Felix L.

PY - 2024/6/5

Y1 - 2024/6/5

N2 - 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.

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 - UT-Hybrid-D

KW - Radiative transfer

KW - Refractive index

KW - Semigroup theory

KW - Well-posedness

KW - Polarization

UR - http://www.scopus.com/inward/record.url?scp=85185577570&partnerID=8YFLogxK

U2 - 10.1016/j.jde.2024.02.022

DO - 10.1016/j.jde.2024.02.022

M3 - Article

AN - SCOPUS:85185577570

SN - 0022-0396

VL - 393

SP - 174

EP - 203

JO - Journal of differential equations

JF - Journal of differential equations

ER -

On the unique solvability of radiative transfer equations with polarization

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Keywords

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