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Transport equation on a finite domain. II: Reduction to X- and Y- functions. (English) Zbl 0527.45004


MSC:

45K05 Integro-partial differential equations
45E10 Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type)
82C70 Transport processes in time-dependent statistical mechanics
85A25 Radiative transfer in astronomy and astrophysics
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[1] V.A. Ambartsumian: On the question of the diffuse reflection of light by an opaque medium. Dokl. Akad. Nauk SSSR 38(8), 257–262, 1943 (Russian).
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[4] I.W. Busbridge, S.E. Orchard: Reflection and transmission of light by thick atmospheres of pure scatterers with a phase function \(1 + \mathop \Sigma \limits_{n = 1}^N \overline w n Pn\) (cos{\(\theta\)}). The Astrophysical Journal 154, 729–739, 1968n=1. · doi:10.1086/149792
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[9] J.W. Hovenier: A unified treatment of the reflected and transmitted intensities of a homogeneous plane-parallel atmosphere. Astron. Astrophys. 68, 239–250, 1978.
[10] J.W. Hovenier: Reduction of the standard problem in radiative transfer for a medium of finite optical thickness. Astron. Astrophys. 82, 61–72, 1980.
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[13] C.V.M. van der Mee: Linearized BGK and neutron transport equations on finite domains. Transport Theory and Statistical Physics 10, 75–104, 1981. · Zbl 0488.45006 · doi:10.1080/00411458108247959
[14] C.V.M. van der Mee: Transport Theory in Lp-spaces. To appear in: Integral Equations and Operator Theory. · Zbl 0506.45011
[15] C.V.M. van der Mee: Transport Equation on a finite domain. I. Reflection and transmission operators and diagonalization. Submitted at: Integral Equations and Operator Theory. · Zbl 0527.45003
[16] T.W. Mullikin: A complete solution of the X- and Y-equations of Chandrasekhar. The Astrophysical Journal 136, 627–635, 1962. · doi:10.1086/147413
[17] T.W. Mullikin: Chandrasekhar’s X- and Y-functions. Trans. A.M.S. 112, 316–322, 1964.
[18] T.W. Mullikin: Radiative transfer in finite homogeneous atmospheres with anisotropic scattering. II. The uniqueness problem for Chandrasekhar’s {\(\psi\)} and equations. The Astrophysical Journal 139, 1267–1289, 1964. · doi:10.1086/147864
[19] N.I. Muskhelishvili: Singular integral equations. Groningen (The Netherlands), Noordhoff, 1953=Moscow, ”Nauka”, 1967 (Russian).
[20] S. Pahor: A new approach to half-space transport problems. Nuclear science and engineering 26, 192,197, 1966.
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