The work presents the analysis of the free boundary value problem related to
the invasion model of new species in biofilm reactors. 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 and a system of semi-linear elliptic
partial differential equations describing the substrate trends. The model is
completed with a system of elliptic partial differential equations governing
the diffusion and reaction of planktonic cells, which are able to switch their
mode of growth from planktonic to sessile when specific environmental
conditions are found. Two systems of nonlinear differential equations for the
substrate and planktonic cells mass balance within the bulk liquid are also
considered. The free boundary evolution is governed by a differential equation
that accounts for detachment. The qualitative analysis is performed and a
uniqueness and existence result is discussed. Furthermore, two special models
of biological and engineering interest are discussed numerically. The invasion
of Anammox bacteria in a constituted biofilm inhabiting the deammonification
units of the wastewater treatment plants is simulated. Numerical simulations
are run to evaluate the influence of the colonization process on biofilm
structure and activity.Comment: 20 pages, 11 figures, original pape
