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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2603.10531 |
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- 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.