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

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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.

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Acknowledgements

The authors would like to thank the anonymous referee for a careful reading of the manuscript and several helpful comments which contributed to improve the presentation of the paper. Sheng-Ya Feng is partially supported by the National Natural Science Foundation of China (Grant Nos. 11501203 and 11426109), the China Postdoctoral Science Foundation (Grant No. 2016M600278), and the National Foundation of China Scholarship Council (Grant No. 201806745028). Der-Chen Chang is partially supported by an NSF Grant DMS-1408839 and a McDevitt Endowment Fund at Georgetown University.

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Authors and Affiliations

  1. School of Mathematical Sciences and Key Lab of Mathematics for Nonlinear Science, Fudan University, Shanghai, 200433, People’s Republic of China

    Sheng-Ya Feng

  2. Department of Mathematics, East China University of Science and Technology, Shanghai, 200237, People’s Republic of China

    Sheng-Ya Feng

  3. Department of Mathematics and Statistics, Georgetown University, Washington, DC, 20057, USA

    Der-Chen Chang

  4. Graduate Institute of Business Administration, College of Management, Fu Jen Catholic University, New Taipei City, 242, Taiwan, ROC

    Der-Chen Chang

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  1. Sheng-Ya Feng
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Feng, SY., Chang, DC. Existence, uniqueness, and approximation solutions to linearized Chandrasekhar equation with sharp bounds. Anal.Math.Phys. 10, 17 (2020). https://doi.org/10.1007/s13324-020-00359-2

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