Co-existence of traveling waves for a model of microbial growth and competition in a flow reactor (Q1030542)

Understanding conditions under which a population of micro-organisms can survive as well as co-exist in a flow reactor is an important issue. The author considers a reaction-diffusion model for a microbial flow reactor with two competing species. It is supposed that the amount of nutrient is input in a constant velocity at one end of the flow and is washed out at the other end of the reactor. The dynamical behavior of the population growth of these two species is studied with particular emphasis on the coexistence of traveling waves that best describes the long time dynamical behavior. By developing shooting method and continuation argument with the aid of an appropriately Lyapunov function, sufficient conditions for the coexistence of traveling waves as well as the minimum wave speed are obtained.