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Analysis of a moving boundary value problem arising in biofilm modelling
Author(s) -
Szomolay Barbara
Publication year - 2008
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.1000
Subject(s) - uniqueness , mathematics , biofilm , boundary value problem , biocide , steady state (chemistry) , boundary (topology) , value (mathematics) , mathematical analysis , calculus (dental) , chemistry , statistics , bacteria , medicine , organic chemistry , dentistry , genetics , biology
We consider a moving boundary value problem associated with a 1‐D biofilm model proposed by Szomolay et al. ( Environ. Microbiol. 2005; 8 :1186–1191). The new model includes growth and detachment which make it more realistic in a biofilm setting. Global existence and properties of solutions are shown using the method of characteristics. We also study the existence of the corresponding steady‐state solutions and prove their uniqueness for small doses of biocide. In addition, sufficient conditions for the existence of trivial/nontrivial steady states are established. Copyright © 2008 John Wiley & Sons, Ltd.