Existence analysis for a reaction-diffusion Cahn–Hilliard-type system with degenerate mobility and singular potential modeling biofilm growth

The global existence of bounded weak solutions to a diffusion system modeling biofilm growth is proven. equations consist reaction-diffusion equation for the substrate concentration and fourth-order Cahn–Hilliard-type volume fraction biomass, considered in domain with no-flux boundary conditions. main difficulties are coming from degenerate diffusivity mobility, singular potential arising logarithmic free energy, nonlinear reaction rates. These issues overcome by truncation technique Browder–Minty trick identify limits terms. qualitative behavior illustrated numerical experiments one space dimension, using BDF2 (second-order backward Differentiation Formula) finite-volume scheme.