title: On a multiphase multicomponent model of biofilm growth.
abstract: 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 regionΩ(t), and the solvent in the surrounding regionD(t). The interface between the two regions,Γ(t), is a free boundary. In this paper, we consider a mathematical model, which consists of a Stokes equation for the EPS with bacteria attached to it, and a Stokes equation for the solvent inΩ(t) and a different one for the solvent inD(t). The volume fraction of the EPS is another unknown satisfying a reaction-diffusion equation. The entire system is coupled nonlinearly withinΩ(t), and across the free surfaceΓ(t). We prove the existence and uniqueness of solution, with a smooth surfaceΓ(t), for a small time interval.
authors.affiliation: Mathematical Biosciences Institute, and Department of Mathematics, Ohio State University, Columbus, Ohio 43210.
authors.forename: A
authors.initials: A
authors.lastname: Friedman
authors.affiliation: Department of Applied and Computational Mathematics and Statistics, University of Notre Dame, IN 46556.
authors.forename: Bei
authors.initials: B
authors.lastname: Hu
authors.affiliation: Mathematical Biosciences Institute, and Department of Mathematics, Ohio State University, Columbus, Ohio 43210.
authors.forename: Chuan
authors.initials: C
authors.lastname: Xue
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