Analysis of a one-dimensional biofilm model
Abstract
In this paper a reduced one-dimensional moving boundary model is studied that describes the evolution of a biofilm driven by the presence of a reaction limiting substrate. Global well-posedness is established for the resulting parabolic free boundary value problem in strong form in Sobolev spaces and for a quasi-stationary approximation in spaces of classical regularity. The general existence results are complemented by results about the qualitative properties of solutions including the existence, in general, and, additionally, the uniqueness and stability of non-trivial equilibria, in a special case.
Fields of Study & Subjects
Mathematical Biology Tumor Growth
Stability and Controllability of Differential Equations
Bacterial biofilms and quorum sensing
Publication details
- Journal / source
- Quarterly of Applied Mathematics
- Volume
- 84
- Issue
- 3
- Pages
- 537–559
- Publication date
- 14 April 2026
- Language
- EN