โ Scribed by A.E. Kovtanyuk; I.V. Prokhorov
No coin nor oath required. For personal study only.
A boundary-value problem for the polarized-radiation transfer equation for a layered medium with Fresnel matching conditions at the boundaries of the medium partition is examined. The theorems of solvability of the boundary-value problem are proved, and the continuity properties for its solution are examined. A numerical algorithm based on the Monte Carlo method for solving the boundary-value problem is proposed and proved.
๐ SIMILAR VOLUMES
The problem under investigation is the heat equation in the upper half-plane, to which the diffusion in the longitudinal direction has been suppressed, and augmented with a nonlinear oblique derivative condition. This paper proves global existence and qualitative properties to the Cauchy problem for
In this paper, we deal with a class of pseudoparabolic problems with integral boundary conditions. We will first establish an a priori estimate. Then, we prove the existence, uniqueness and continuous dependence of the solution upon the data. Finally, some extensions of the problem are given.
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