生物膜形成的数学模型
Mathematical Modeling of Biofilm Development
摘要：
我们进行数学分析的生物膜的发展过程。提出了一个描述生物量生长的模型：它产生于耦合三个抛物型非线性方程：退化和奇异扩散的生物量方程，与生物量密度相关扩散的营养输送方程，和Navier-Stokes型方程，描述生物膜发展的流体流动。这种流动受到生物量-密度依赖性障碍的影响。该模型被视为一个系统的三个包含，或变分不等式，第三个原因是系统的可解性的主要困难。我们的方法是基于Navier-Stokes变分不等式理论的最新发展。
英文摘要：
We perform mathematical anaysis 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 tranport 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 third one causes major difficulties for the system's solvability. Our approach is based on the recent development of the theory on Navier-Stokes variational inequalities.
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