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 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, which consists of a Stokes equation for the EPS with bacteria attached to it, and a Stokes equation for the solvent in Ω(t) and a different one 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 solution, with a smooth surface Γ(t), for a small time interval.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
