Existence, uniqueness, and approximation solutions to linearized Chandrasekhar equation with sharp bounds

Abstract

This article continues to study the linearized Chandrasekhar equation. We use the Hilbert-type inequalities to accurately calculate the norm of the Fredholm integral operator and obtain the exact range for the parameters of the linearized Chandrasekhar equation to ensure that there is a unique solution to the equation in $$L^p$$ space. A series of examples that can accurately calculate the norm of Fredholm integral operator shows that the Chandrasekhar kernel functions do not need to meet harsh conditions. As the symbolic part of the Chandrasekhar kernel function and the non-homogeneous terms satisfy the exponential decay condition, we yield a normed convergence rate of the approximation solution in $$L^p$$ sense, which adds new results to the theory of radiation transfer in astrophysics.