naa a22 4500 51081249X CHVBK 20180411083449.0 cr unu---uuuuu 180411e20130601xx s 000 0 eng 10.1134/S0081543813050118 doi (NATIONALLICENCE)springer-10.1134/S0081543813050118 Panasenko G. Institut Camille Jordan UMR CNRS 5208 et Structure Fédérative de Recherche Modélisation Mathématique MODMAD 4169, Université de Saint-Etienne, rue Paul Michelon 23, 42023, Saint-Etienne, France aut Partial asymptotic decomposition of the domain for the diffusion-discrete absorption equation [Elektronische Daten] [G. Panasenko] We consider the diffusion-discrete absorption equation, which is an approximate model of the diffusion of a substance in a solution containing a chain of cells absorbing the substance; the size of the cells is much smaller than the distance h between them, and this distance is small compared to the length of the chain. The diffusion-discrete absorption equation contains the standard diffusion term and a discrete point absorption, which is described by the sum of a large number of Dirac delta functions with supports on a nonuniform grid multiplied by an unknown function (concentration). We study the possibility of a partial asymptotic decomposition of the domain for the diffusion-discrete absorption equation: it is required to preserve the discrete description of the absorption on a part of the domain and pass to a continuous description on the greater part of the domain. This combination of the macroscopic and microscopic descriptions in one model is characteristic of multiscale modeling. We obtain an error estimate for the partially continuous model with respect to the original model with completely discrete absorption. Pleiades Publishing, Ltd., 2013 partial asymptotic decomposition nationallicence discrete-continuum models nationallicence diffusion equation nationallicence error estimate nationallicence Proceedings of the Steklov Institute of Mathematics SP MAIK Nauka/Interperiodica 281(2013-06-01), 118-125 0081-5438 281<118 2013 281 11501 https://doi.org/10.1134/S0081543813050118 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1134/S0081543813050118 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Panasenko G. Institut Camille Jordan UMR CNRS 5208 et Structure Fédérative de Recherche Modélisation Mathématique MODMAD 4169, Université de Saint-Etienne, rue Paul Michelon 23, 42023, Saint-Etienne, France aut NATIONALLICENCE 773 0- Proceedings of the Steklov Institute of Mathematics SP MAIK Nauka/Interperiodica 281(2013-06-01), 118-125 0081-5438 281<118 2013 281 11501 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer