Premium
Analysis of a bacterial model with nutrient‐dependent degenerate diffusion
Author(s) -
Horger Thomas,
Kuttler Christina,
Wohlmuth Barbara,
Zhigun Anna
Publication year - 2014
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3322
Subject(s) - degenerate energy levels , uniqueness , reaction–diffusion system , mathematics , multicellular organism , diffusion , biofilm , biological system , bacteria , mathematical analysis , chemistry , biology , physics , thermodynamics , biochemistry , genetics , quantum mechanics , gene
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. Copyright © 2014 John Wiley & Sons, Ltd.