Analysis of a one-dimensional biofilm model

Patrick Guidotti; Christoph Walker

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arXiv · 2505.23545

Analysis of a one-dimensional biofilm model

Patrick Guidotti·Christoph Walker

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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.

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Patrick Guidotti, Christoph Walker. 2025-05-29. Analysis of a one-dimensional biofilm model. https://arxiv.org/abs/2505.23545

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