caa a22 4500 605524246 CHVBK 20210128100753.0 cr unu---uuuuu 210128e20150401xx s 000 0 eng 10.1007/s10958-015-2311-y doi (NATIONALLICENCE)springer-10.1007/s10958-015-2311-y Diffraction by a Grating Consisting of Absorbing Screens of Different Height. New Equations [Elektronische Daten] [A. Korolkov, A. Shanin] The problem of diffraction of a plane wave by a grating consisting of absolutely absorbing screens of different height is studied. It is assumed that the angle of incidence is small. The problem is considered in the parabolic approximation. Edge Green functions are introduced. An embedding formula and a spectral equation for the edge Green functions are derived. An OE-equation for the coefficients of the spectral equation is constructed. The latter is solved numerically. The evolution equation describing the dependence of the edge Green functions on a geometric parameter (the height of the screens) is proved. Using this equation, the asymptotics of the reflection coefficient is calculated for the principal mode. Springer Science+Business Media New York, 2015 Korolkov A. Moscow Lomonosov State University, Moscow, Russia aut Shanin A. Moscow Lomonosov State University, Moscow, Russia aut Journal of Mathematical Sciences Springer US; http://www.springer-ny.com 206/3(2015-04-01), 270-287 1072-3374 206:3<270 2015 206 10958 https://doi.org/10.1007/s10958-015-2311-y text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10958-015-2311-y text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Korolkov A. Moscow Lomonosov State University, Moscow, Russia aut NATIONALLICENCE 700 1- Shanin A. Moscow Lomonosov State University, Moscow, Russia aut NATIONALLICENCE 773 0- Journal of Mathematical Sciences Springer US; http://www.springer-ny.com 206/3(2015-04-01), 270-287 1072-3374 206:3<270 2015 206 10958