Analysis of a bacterial model with nutrient‐dependent degenerate diffusion. (1st December 2014)

• Record Type: Journal Article
• Authors: Horger, Thomas; Kuttler, Christina; Wohlmuth, Barbara; Zhigun, Anna
• Is Part Of: Mathematical methods in the applied sciences. Volume 38:Number 17(2015:Nov. 30)
• Page Start: 3851
• Page End: 3865
• Publication Date: 2014-12-01
• Subjects: biofilms -- degenerate diffusion -- parabolic system -- pattern formation -- weak solution -- well‐posedness; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.3322
• Languages: English
• ISSNs: 0170-4214

Abstract

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. Copyright © 2014 John Wiley & Sons, Ltd.