Biofilms are formed when free-floating bacteria attach to a surface and secrete polysaccharide to form an extracellular polymeric matrix (EPS). A general model of biofilm growth needs to include the bacteria, the EPS, and the solvent within the biofilm region Ω(t), and the solvent in the surrounding region D(t). The interface between the two regions, Γ(t), is a free boundary. In this paper, we consider a mathematical model that consists of a Stokes equation for the EPS with bacteria attached to it, a Stokes equation for the solvent in Ω(t) and another for the solvent in D(t). The volume fraction of the EPS is another unknown satisfying a reaction-diffusion equation. The entire system is coupled nonlinearly within Ω(t) and across the free surface Γ(t). We prove the existence and uniqueness of a solution, with a smooth surface Γ(t), for a small time interval.

中文翻译：

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关于生物膜生长的多相多组分模型

当自由漂浮的细菌附着在表面并分泌多糖以形成细胞外聚合物基质 (EPS) 时，就会形成生物膜。生物膜生长的一般模型需要包括细菌、EPS 和生物膜区域 Ω(t) 内的溶剂，以及周围区域 D(t) 中的溶剂。两个区域之间的界面 Γ(t) 是一个自由边界。在本文中，我们考虑了一个数学模型，该模型由附着有细菌的 EPS 的斯托克斯方程、Ω(t) 中溶剂的斯托克斯方程和 D(t) 中溶剂的另一个斯托克斯方程组成。EPS 的体积分数是另一个满足反应扩散方程的未知数。整个系统在 Ω(t) 内和跨自由表面 Γ(t) 非线性耦合。我们证明了具有光滑表面Γ(t)的解的存在性和唯一性，