Abstract
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 language | English |
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Pages (from-to) | 3851-3865 |
Journal | Mathematical Methods in the Applied Sciences |
Volume | 38 |
Issue number | 17 |
Early online date | 01 Dec 2014 |
DOIs | |
Publication status | Published - 30 Nov 2015 |
Keywords
- biofilms
- degenerate diffusion
- parabolic system
- pattern formation
- weak solution
- well-posedness
ASJC Scopus subject areas
- General Mathematics
- General Engineering