Analysis of a bacterial model with nutrient‐dependent degenerate diffusion | Zendy

Horger Thomas | Zendy; Kuttler Christina | Zendy; Wohlmuth Barbara | Zendy; Zhigun Anna | Zendy

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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.

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