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Nonstationary radiation transfer through a multilayered medium with reflection and refraction conditions
Author(s) -
Amosov Andrey
Publication year - 2018
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.5272
Subject(s) - uniqueness , refraction , reflection (computer programming) , mathematics , radiation , a priori and a posteriori , boundary value problem , mathematical analysis , radiative transfer , optics , physics , computer science , programming language , philosophy , epistemology
We consider an initial‐boundary value problem for the radiation transfer equation with reflection and refraction conditions describing a nonstationary process of the radiation transfer in multilayered semitransparent for radiation medium, consisting of m parallel vertical layers. We establish the existence and uniqueness of a solution for the problem with data from the spaces of L p type, 1 ≤ p ≤ ∞ . We also obtain a priori estimates for the solution and prove an exponential stabilization of the solution as T → ∞ .