Mathematical modeling of biofilm development

被引：4

作者：

Gokieli, Maria ^{[1
]}

Kenmochi, Nobuyuki ^{[1
]}

Niezgodka, Marek ^{[1
]}

机构：

[1] Univ Warsaw, Interdisciplinary Ctr Math & Computat Modelling, Pawinskiego 5a, PL-02106 Warsaw, Poland

来源：

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS | 2018年 / 42卷

关键词：

Navier; -Stokes; Degenerate diffusion; Obstacle; Flow; Variational inequality; Subdifferential;

D O I：

10.1016/j.nonrwa.2018.01.005

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We perform mathematical analysis of the biofilm development process. A model describing biomass growth is proposed: It arises from coupling three parabolic nonlinear equations: a biomass equation with degenerate and singular diffusion, a nutrient transport equation with a biomass-density dependent diffusion, and an equation of the Navier-Stokes type, describing the fluid flow in which the biofilm develops. This flow is subject to a biomass' density-dependent obstacle. The model is treated as a system of three inclusions, or variational inequalities; the equation of the Navier-Stokes type causes major difficulties for the system's solvability. Our approach is based on the recent development of the theory on Navier-Stokes variational inequalities. (C) 2018 Elsevier Ltd. All rights reserved.

引用

页码：422 / 447

页数：26

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