On the unique solvability of radiative transfer equations with polarization. (English) Zbl 1536.35207
Summary: 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.
MSC:
| 35L50 | Initial-boundary value problems for first-order hyperbolic systems |
| 35B09 | Positive solutions to PDEs |
| 35L60 | First-order nonlinear hyperbolic equations |
| 46E35 | Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems |
| 47A63 | Linear operator inequalities |
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