Analysis of a Biofilm Model in a Continuously Stirred Tank Reactor with Wall Attachment

TL;DR

This paper presents a mathematical analysis of a biofilm model in a stirred tank reactor, focusing on stability and long-term behavior of bacterial populations with wall attachment.

Contribution

It introduces a coupled free-boundary and ODE model for biofilm dynamics, providing new insights into stability and equilibrium conditions.

Findings

Global well-posedness established

Conditions for stability of equilibria derived

Existence of nontrivial equilibrium proven

Abstract

We investigate a mathematical model for a bacterial population in a continuously stirred tank reactor with wall attachment. The model couples a free-boundary value problem for substrate diffusion in the one-dimensional biofilm with a system of nonlinear ODEs for biofilm thickness, suspended biomass, and free substrate concentration. We establish global well-posedness and analyze the long-term dynamics. In particular, we characterize the local and global stability of the trivial (washout) equilibrium, prove the existence of a nontrivial equilibrium, and, under additional structural assumptions, establish its uniqueness and derive conditions for its local stability.