Mohammad Asadpour Faziallahi
Karim Ivaz

The initial attached cell layer in multispecies bio lm growth is considered. Thecorresponding mathematical model leads to discuss a free boundary problem for asystem of nonlinear hyperbolic partial di erential equations, where the initial bioflmthickness is equal to zero. No assumptions on initial conditions for biomass concen-trations and bio lm thickness are required. The data that the problem needs are theconcentration of biomass in the bulk liquid and biomass fux from the bulk liquid.The di erential equations are converted into an equivalent system of Volterra integralequations. we use numerical method to solve the nonlinear system of Volterra integralequations (SVIEs) of the second kind. This method converts the nonlinear system ofintegral equations into a linear integral equation at each step.

free boundary problem, nonlinear system of Volterra integral equations, bioflm