The principal eigenvalue for a time-space periodic reaction-diffusion-advection equation with delay nutrient recycling

In this paper, we propose and analyze a growth model of autotrophic microorganism, which is a time-space periodic reaction-diffusion-advection equation with delay nutrient recycling. First, by the linear chains technique, we transform the reaction-diffusion-advection model with a distributed delay into the equivalent system without distributed delay, then, we establish the existence of the principal eigenvalue of this system, it is a basic tool to study the reaction-diffusion-advection equation. Finally, some conclusions are given.