Analysis of a bacterial model with nutrient-dependent degenerate diffusion

Thomas Horger, Christina Kuttler, Barbara Wohlmuth, Anna Zhigun*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)


We introduce and study a degenerate reaction-diffusion system that can serve as a model prototype for the pattern formation of a bacterial multicellular community where the bacteria produce biofilm, grow and spread in the presence of a nutrient. Under proper conditions on the reaction terms, we prove the global existence and the uniqueness of solutions and illustrate the possible model behaviour in numerical simulations for a two-dimensional setting.

Original languageEnglish
Pages (from-to)3851-3865
JournalMathematical Methods in the Applied Sciences
Issue number17
Early online date01 Dec 2014
Publication statusPublished - 30 Nov 2015


  • biofilms
  • degenerate diffusion
  • parabolic system
  • pattern formation
  • weak solution
  • well-posedness

ASJC Scopus subject areas

  • General Mathematics
  • General Engineering


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