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Solution of the general boundary-value problem in the transfer theory for a plane layer with a horizontal nonuniformity. (English. Russian original) Zbl 0870.35109

Phys.-Dokl. 39, No. 11, 740-744 (1994); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 339, No. 2, 171-175 (1994).
Consider the transfer operator \[ D=D_z+\sin\theta\cos\varphi {\partial\over\partial x}+\sin\theta\sin\varphi {\partial\over\partial y}, \] where \(D_z=\mu{\partial\over\partial z}+ \sigma_{\text{tot}}(z)\) and the collision integral \[ S\phi= \sigma_{\text{seat}}(z) \int_\Omega\gamma(z,s,s')\phi(z,r_\perp,s')ds'. \] The boundary-value problem \(K\phi=0,\quad\phi|_t=0,\quad\phi|_b= E(r_\perp,s)\) is investigated. Here \(K=D-S\), \(t=\{z,r_\perp,s;z=0\}\), \(b=\{z,r_\perp,s;z=H\}\), \(r_\perp=(x,y)\).

MSC:

35Q60 PDEs in connection with optics and electromagnetic theory
82C70 Transport processes in time-dependent statistical mechanics
65Z05 Applications to the sciences
78A45 Diffraction, scattering
85A25 Radiative transfer in astronomy and astrophysics
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