naa a22 4500 510812538 CHVBK 20180411083449.0 cr unu---uuuuu 180411e20130601xx s 000 0 eng 10.1134/S0081543813050040 doi (NATIONALLICENCE)springer-10.1134/S0081543813050040 El'bert A. Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, ul. S. Kovalevskoi 16, 620990, Yekaterinburg, Russia aut Asymptotic analysis of the diffusion-absorption equation with fast and strongly oscillating absorbtion coefficient in the two-dimensional case [Elektronische Daten] [A. El'bert] The Helmholtz equation with fast oscillating absorbtion coefficient and constant reflection coefficient is considered. The equation models light absorption in a medium containing a periodic set of fine blood vessels. It is assumed that the absorption takes place only inside the vessels. It is also assumed that the reflection coefficient is constant whereas the absorbtion coefficient is small everywhere except for a set of periodic thin strips modeling blood vessels, where the absorption coefficient equals a large parameter ω. There are two other parameters in the problem: ɛ is the ratio of the distance between the vessel axes to the characteristic macroscopic size, and δ is the ratio of the width of the fine vessels to the period. Both parameters ɛ and δ are assumed to be small. The main result is the construction of an asymptotic solution. Pleiades Publishing, Ltd., 2013 asymptotics nationallicence Helmholtz equation nationallicence homogenization nationallicence Proceedings of the Steklov Institute of Mathematics SP MAIK Nauka/Interperiodica 281(2013-06-01), 36-43 0081-5438 281<36 2013 281 11501 https://doi.org/10.1134/S0081543813050040 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1134/S0081543813050040 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- El'bert A. Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, ul. S. Kovalevskoi 16, 620990, Yekaterinburg, Russia aut NATIONALLICENCE 773 0- Proceedings of the Steklov Institute of Mathematics SP MAIK Nauka/Interperiodica 281(2013-06-01), 36-43 0081-5438 281<36 2013 281 11501 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer