Existence and stability of a steady state for a coupled system of elliptic equation modelling the biodenitrification process

Abstract

The process of biodegradation requires the success of bacteria to colonize the reactor. In this work, we will give a sufficient condition, which is the minimum amount of nutrient that must be injected into the reactor for the bacteria to evolve, for the existence and stability of a steady state other than the washout steady state, for a coupled system of partial differential equations (PDE) modelling the bio‐denitrification process. The existence of a weak steady state is showed contrary to what is done for the ordinary differential equation (ODE) because our system consists of a coupled partial differential equations (PDE). The stability of this steady state depends on the stability of the washout steady state which is, more or less, easy to study.