Analysis of a degenerate biofilm model with a nutrient taxis term

Hermann J. Eberl, Messoud A. Efendiev, Dariusz Wrzosek, Anna Zhigun

Research output: Contribution to journalArticlepeer-review

9 Citations (Scopus)


We introduce and analyze a prototype model for chemotactic effects in biofilm formation. The model is a system of quasilinear parabolic equations into which two thresholds are built in. One occurs at zero cell density level, the second one is related to the maximal density which the cells cannot exceed. Accordingly, both diffusion and taxis terms have degenerate or singular parts. This model extends a previously introduced degenerate biofilm model by combining it with a chemotaxis equation. We give conditions for existence and uniqueness of weak solutions and illustrate the model behavior in numerical simulations.

Original languageEnglish
Pages (from-to)99-119
JournalDiscrete and Continuous Dynamical Systems- Series A
Issue number1
Publication statusPublished - 01 Jan 2014


  • Biofilm
  • Chemotaxis
  • Compactness method
  • Degenerate diffusion
  • Fast diffusion
  • Singular quasilinear parabolic equation

ASJC Scopus subject areas

  • Analysis
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics


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