Analysis of a moving boundary value problem arising in biofilm modelling

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 (C) 2008 John Wiley & Sons, Ltd.