Abstract
In this paper, we are concerned with a diffusive flocculation model in heterogeneous environment. We proved global existence and coexistence of species in the medium. Stability of the washout steady state was shown by analyzing the sign of the principal eigenvalue corresponding to the trivial solution. And, by numerical simulations, we illustrate the convergence towards the washout steady state as diffusion becomes small or towards the coexistence of species as diffusion becomes large under some appropriate assumptions on mortality coefficients showing the effect of diffusion coefficient on the coexistence of microbial species. Our arguments rely on the invariant region method, the lower and upper solutions method and the spectral theory.