  A free boundary value problem related to the genesis of multispecies granular
biofilms is presented. The granular biofilm is modelled as a spherical free
boundary domain with radial symmetry. The proposed model is conceived in the
framework of continuum mechanics and consists of: nonlinear hyperbolic PDEs
which model the advective transport and growth of attached species that
constitute the granular biofilm matrix; semilinear elliptic PDEs which govern
the diffusive transport and conversion of nutrients; and semilinear elliptic
PDEs describing the invasion phenomena and conversion of planktonic cells
suspended in the surrounding environment. The evolution of the free boundary is
governed by an ODE accounting for microbial growth, attachment, and detachment.
By using the method of characteristics, the system of equations constituting
the granular biofilm model is converted into an equivalent integral system.
Existence and uniqueness of solutions are discussed and proved for the
attachment regime using the fixed point theorem.
