The classical problem of radiative transfer with the escape of a photon from a semi-infinite scattering and absorbing atmosphere is generalized by the author to the case where the time expended by photons in multiple scattering in it is taken into account. The possibility of a variational formulation of the problem and the generalization of quadratic and bilinear conservation laws obtained in the stationary problem is raised. It is shown that the general statement of the problem does not allow this formulation owing to the nonpotentiality of the resulting differential operator; however, it is possible in the special case of conservative scattering. The resulting two conservation laws reflect the fact that the medium is homogeneous and time is isotropic.
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Translated from Astrofizika, Vol. 65, No. 1, pp. 95-105 (February 2022)
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Nikhoghossian, A.G. Conservation Laws in Time-Dependent Radiative Transfer Problems. Astrophysics 65, 81–92 (2022). https://doi.org/10.1007/s10511-022-09723-5
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DOI: https://doi.org/10.1007/s10511-022-09723-5