Positivity and monotonicity properties of transport equations with spatially dependent cross sections

Mee, C. V. M. van der

doi:10.1080/00411458208245741

Cited by 5 publications

(1 citation statement)

References 9 publications

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“…The equivalence between the boundary value problem (1.12) -(1.1 3) and o ( r ) ( u , q ) = e(b-"/UJ(u,q) If f : [0, b] -+ Hp is a uniformly Holder continuous function, then the reasoning of [28] can be applied to prove the equivalence of (2.5) with right-hand side the convolution equation (2.1 1) is obtained, for instance, by choosing…”

Section: Preliminaries and Equivalence Theoremsmentioning

confidence: 99%

Half‐ and finite‐range completeness for the equation of transfer of polarized light

Mee¹,

Neunzert

1984

Math Methods in App Sciences

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On neglecting reflection by the surface the existence and uniqueness are proved for the solution of the equation of transfer of polarized light in a homogeneous semi‐infinite or finite plane‐parallel medium. A general LL‐space formulation, where 1 ≤ p < ∞, is adopted. The analysis concerns a vector‐valued convolution equation, which is an equivalent form of the equation of radiative transfer and is solved with the help of Wiener‐Hopf factorization, Fredholm index and cone preservation methods. The results are also proved for the equations obtained from the full equation of transfer by means of Fourier expansion and symmetry relations.

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Section: Preliminaries and Equivalence Theoremsmentioning

confidence: 99%

Half‐ and finite‐range completeness for the equation of transfer of polarized light

Mee¹,

Neunzert

1984

Math Methods in App Sciences

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Polarized light transfer above a reflecting surface

Mee

Neunzert

1986

Math Methods in App Sciences

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The existence and uniqueness are established for the solution of the equation of transfer of polarized light in a homogeneous atmosphere of finite optical thickness, assuming reflection by the planetary surface. A general Lp‐space formulation is adopted. The boundary value problem is first written as a vector‐valued integral equation. Using monotonicity properties of the spectral radii of the integral operators involved as well as recent half‐range completeness results for kinetic equations with reflective boundary conditions, the present results follow as a corollary.

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The transformation of PL solutions for extremely anisotropic scattering to solutions with isotropic scattering and application to the critical slab problem

Tezcan

Yildiz

1993

Journal of Quantitative Spectroscopy and Radiative Transfer

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Positivity and monotonicity properties of transport equations with spatially dependent cross sections

Cited by 5 publications

References 9 publications

Half‐ and finite‐range completeness for the equation of transfer of polarized light

Half‐ and finite‐range completeness for the equation of transfer of polarized light

Polarized light transfer above a reflecting surface

The transformation of PL solutions for extremely anisotropic scattering to solutions with isotropic scattering and application to the critical slab problem

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