Homogenization of the diffusion equation with a singular potential for a model of a biological cell network
| Autor: | Latifa Ait Mahiout, Grigory Panasenko, Vitaly Volpert |
|---|---|
| Přispěvatelé: | Laboratoire d'équations aux dérivées partielles non linéaires et histoire des mathématiques [Alger], École normale supérieure - Kouba-Alger (ENS Kouba-Alger), Modélisation mathématique, calcul scientifique (MMCS), Institut Camille Jordan (ICJ), École Centrale de Lyon (ECL), Université de Lyon-Université de Lyon-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Institut National des Sciences Appliquées de Lyon (INSA Lyon), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet - Saint-Étienne (UJM)-Centre National de la Recherche Scientifique (CNRS)-École Centrale de Lyon (ECL), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet - Saint-Étienne (UJM)-Centre National de la Recherche Scientifique (CNRS), Modélisation multi-échelle des dynamiques cellulaires : application à l'hématopoïese (DRACULA), Université de Lyon-Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA)-Université Jean Monnet - Saint-Étienne (UJM)-Centre National de la Recherche Scientifique (CNRS)-Inria Lyon, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), Peoples Friendship University of Russia [RUDN University] (RUDN) |
| Rok vydání: | 2020 |
| Předmět: |
Multicellular structure
Diffusion equation Applied Mathematics General Mathematics Mathematical analysis General Physics and Astronomy 010103 numerical & computational mathematics Biological tissue Limiting Nutrient consumption 01 natural sciences Homogenization (chemistry) Laplacian with Dirac’s potential Quantitative Biology::Cell Behavior 010101 applied mathematics High contrast homogeneization Nonlinear system Biological cell [MATH]Mathematics [math] 0101 mathematics Mathematics |
| Zdroj: | Zeitschrift für Angewandte Mathematik und Physik Zeitschrift für Angewandte Mathematik und Physik, 2020, 71 (6), pp.181. ⟨10.1007/s00033-020-01401-w⟩ |
| ISSN: | 1420-9039 0044-2275 |
| DOI: | 10.1007/s00033-020-01401-w |
| Popis: | The paper is devoted to a reaction-diffusion problem describing diffusion and consumption of nutrients in a biological tissue consisting of small cells periodically arranged in an extracellular matrix. Cells consume nutrients with a rate proportional to cell area and to nutrient concentration. The dependence on the nutrient concentration can be linear or nonlinear. The cells are modeled by a potential approximating the Dirac’s delta-function. The potential has a periodically distributed support of small measure. The problem contains two small parameters: the diameter of a cell and the distance between the cells (in comparison with the characteristic macroscopic size). In the multi-dimensional formulation assuming some restriction on the relation of parameters, we prove convergence of solution of this problem to the solution of a limiting homogenized problem. We show that the problem is non-homogenizable in classical sense if this restriction fails. |
| Databáze: | OpenAIRE |
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