The Sobolev Approximation is a means of approximating the solution to the Radiative Transfer equation under specific challenging conditions, i.e., in gas with a very high velocity gradient. In astrophysics, it is used in the analysis of Spectral Lines, i.e., to model the environment that produces observed lines. The Sobolev Approximation assumes local variation in the velocity gradient are negligible as compared to variations over longer lengths. The Sobolev Length is the distance below which gradations are ignored.
Line Shape Function