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- W1750902231 abstract "In this work we study the radiative transfer equation in the forward-peaked regime in free space. Specifically, it is shown that the equation is well-posed by proving instantaneous regularization of weak solutions for arbitrary initial datum in L 1. Classical techniques for hypo-elliptic operators, such as averaging lemma, are used in the argument. Among the interesting aspects of the proof are the use of the stereographic projection and the presentation of a rigorous expression for the scattering operator given in terms of a fractional Laplace–Beltrami operator on the sphere, or equivalently, a weighted fractional Laplacian analog in the projected plane. Such representations may be used for accurate numerical simulations of the model. As a bonus given by the methodology, we show convergence of Henyey–Greenstein scattering models and vanishing of the solution at time algebraic rate due to scattering diffusion." @default.
- W1750902231 created "2016-06-24" @default.
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- W1750902231 date "2015-06-03" @default.
- W1750902231 modified "2023-09-26" @default.
- W1750902231 title "The Radiative Transfer Equation in the Forward-Peaked Regime" @default.
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- W1750902231 doi "https://doi.org/10.1007/s00220-015-2395-8" @default.
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