Qualitative analysis of the moving boundary problem for a biofilm reactor model

Abstract

The work presents the qualitative analysis of the free boundary value problem related to a biofilm reactor model. In the framework of continuum approach to mathematical modelling of biofilm growth, the problem consists of a system of nonlinear hyperbolic partial differential equations governing the microbial species growth, a system of semilinear elliptic partial differential equations describing the substrate trends, and a system of nonlinear differential equations for the mass balance in the reactor. The free boundary evolution is governed by a differential equation that also accounts for detachment and attachment. The main result is a uniqueness and existence theorem. By using the method of characteristics, the original differential system is converted to Volterra integral equations and then the fixed point theorem is used. The work is completed with numerical simulations describing the free boundary evolution and mainly focused on attachment/detachment process.