Continuum approach to mathematical modelling of multispecies biofilms

The work presents a contribution to the mathematical modelling of formation and growth of multispecies biofilms in the framework of continuum approach, without claiming to be complete. Mathematical models for biofilms often lead to consider free boundary value problems for nonlinear PDEs. The emphasis is on the qualitative analysis, uniqueness and existence of solutions and their main properties. Biofilm life is a complex biological process formed by several phases from the formation, development of colonies, attachment and detachment of microbial mass from (to) biofilm to (from) bulk liquid. Most of these processes are modelled and discussed. Moreover, some problems of interest for engineering and biological applications are considered. Indeed, we discuss the free boundary value problem related to biofilm reactors extensively used in wastewater treatment, and the invasion of new species into an already constituted biofilm with the successive colonizations. The main mathematical methodology used is the method of characteristics. The original differential problem is converted to integral equations. Then, the fixed point theorem is applied.