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arXiv · 2603.10531

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

Katerina Nik·Christoph Walker
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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.

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Katerina Nik, Christoph Walker. 2026-03-11. Analysis of a Biofilm Model in a Continuously Stirred Tank Reactor with Wall Attachment. https://arxiv.org/abs/2603.10531

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