Abstract
We investigate the unique solvability of radiative transfer problems without strictly positive lower bounds on the absorption and scattering parameters. The analysis is based on a reformulation of the transfer equation as a mixed variational problem with penalty term for which we establish the well-posedness. We also prove stability of the solution with respect to perturbations in the parameters. This allows to approximate stationary radiative transfer problems by even-parity formulations even in the case of vanishing absorption. The mixed variational framework used for the analysis also enables a systematic investigation of discretization obtained by Galerkin methods. We show that, in contrast to the full problem, the widely used PN-approximations, and discretizations based on these, are not stable in the case of vanishing absorption. Some consequences and possible remedies yielding stable approximations are discussed.
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