On the well-posedness of the Cauchy problem for the equation of radiative transfer with Fresnel matching conditions

DOI10.1134/S0037446615040151zbMath1332.45010MaRDI QIDQ748484

I. V. Prokhorov, Andreĭ Andreevich Sushchenko

Publication date: 29 October 2015

Published in: Siberian Mathematical Journal (Search for Journal in Brave)

zbMATH Keywords

integro-differential equationsCauchy problemradiative transferHille-Yosida theoremboundary value poblemFresnel matching conditionsnonstationary equations

Mathematics Subject Classification ID

Integro-partial differential equations (45K05) Waves and radiation in optics and electromagnetic theory (78A40) Radiative transfer in astronomy and astrophysics (85A25)

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Cites Work

• Boundary value problem for the radiation transfer equation with diffuse reflection and refraction conditions
• A boundary-value problem for the polarized-radiation transfer equation with Fresnel interface conditions for a layered medium
• On the structure of the continuity set of the solution to a boundary-value problem for the radiation transfer equation
• Positivity in time dependent linear transport theory
• Solvability of the initial-boundary value problem for an integrodifferential equation
• On the solubility of the boundary-value problem of radiation transport theory with generalized conjugation conditions on the interfaces
• The cauchy problem for the radiative transfer equation with generalized conjugation conditions
• Boundary value problem of radiation transfer in an inhomogeneous medium with reflection conditions on the boundary
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